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Microtubule architecture: inspiration for novel carbon nanotube-based biomimetic materials
Opinion
Microtubule architecture: inspiration for novel carbon nanotube-based biomimetic materials Francesco Pampaloni1 and Ernst-Ludwig Florin2 1 2
Cell Biology and Biophysics Unit, European Molecular Biology Laboratory, Meyerhofstrasse 1, D-69117 Heidelberg, Germany Center for Nonlinear Dynamics, University of Texas, Austin, TX 78712, USA
Microtubules are self-assembling biological nanotubes that are essential for cell motility, cell division and intracellular trafficking. Microtubules have outstanding mechanical properties, combining high resilience and stiffness. Such a combination allows microtubules to accomplish multiple cellular functions and makes them interesting for material sciences. We review recent experiments that elucidate the relationship between molecular architecture and mechanics in microtubules and examine analogies and differences between microtubules and carbon nanotubes, which are their closest equivalent in nanotechnology. We suggest that a longterm goal in bionanotechnology should be mimicking the properties of microtubules and microtubule bundles to produce new functional nanomaterials. Introduction Microtubules are cytoskeletal biopolymers that, along with actin and intermediate filaments, accomplish essential functions at each stage of the cell’s life cycle. They ensure the mechanical stability of the mitotic spindle, provide oriented tracks for intracellular trafficking of organelles and support the cell’s shape during migration [1]. At the cell length scale, microtubules are very stiff filaments. The average Young’s modulus of a microtubule, considered as a simple isotropic tube, is 2 GPa. Thus, microtubules are as stiff as hard plastic and about one hundred times stiffer than the other cytoskeleton components, actin and intermediate filaments [1]. Interestingly, microtubules are not only stiff, but also highly resilient. Their efficient combination of high stiffness (relative to the other cytoskeletal filaments) and resilience is due to the anisotropic molecular architecture of microtubules and allows them to accomplish multiple tasks in the cell. On the one hand, high stiffness is required to resist the large pushing forces occurring during mitotic spindle elongation at the end of anaphase. On the other hand, high resilience allows microtubules to search the cellular space laterally for binding partners and to keep growing in a different direction without breaking when encountering obstacles. As microtubules are extraordinarily versatile structures, the question arises of what could be learned from them for the design of novel structural and multifunctional Corresponding authors: Pampaloni, F. ([email protected]); Florin, E.-L. ([email protected]).
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materials for applications in material sciences and bionanotechnology. Carbon nanotubes (CNTs), one of the most promising products of nanotechnology, are the closest technological counterpart of microtubules. CNTs are an extremely stiff material; their Young’s modulus is 1 TPa, about five times higher than that of steel (210 GPa) [2]. Similar to microtubules, CNTs are also highly resilient. It is generally acknowledged that CNTs will play a major role in the development of new materials, with applications ranging from ‘super-tough’ composite fibers [3] to drug-delivery systems [4]. Molecular control over the CNT assembly process would be desirable for the full exploitation of their nanoscale properties and for the reproducible fabrication of CNT-based materials. However, although CNTs aggregate into bundles or sheets spontaneously, their assembly into designed composite structures remains difficult to understand and to direct at molecular level. Microtubules and CNTs are surprisingly similar in their mechanical behavior despite their very different chemical composition (proteins and non-covalent interactions in the case of microtubules, carbon and covalent bonds in the case of CNTs) and elastic moduli. Here, we describe key structural aspects of microtubules and review recent results on their mechanics. We then compare CNTs and microtubules side-by-side with respect to structural and elastic properties. Finally, we discuss examples of how microtubules and microtubule-based structures could provide insights for the design and assembly of novel CNT-based biomimetic materials. Structure of microtubules The basic building unit of microtubules is the heterodimeric protein tubulin, consisting of a and b subunits. Tubulin dimers self-assemble head-to-tail (-ab-ab-) into linear protofilaments (PFs) (Figure 1). The cylindrical wall most commonly comprises 13 PFs in vivo, but this number can vary from 9 to 16 in vitro [5]. Tubulins of adjacent PFs are laterally linked through homologous monomer contacts a-a, b-b (except at the ‘seam’, Figure 1). In the microtubule, stacked PFs are slightly longitudinally displaced with respect to each other (0.9 nm in a 13-PF microtubule). This displacement results in a left-handed helical surface lattice. Although the biological function of
0167-7799/$ – see front matter ß 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.tibtech.2008.03.002 Available online 21 April 2008
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Figure 1. Polymerization of microtubules. Tubulin dimers assemble ‘head-to-tail’, forming oligomers that elongate into protofilaments. As the protofilaments reach an estimated critical length of 12 2 dimers [65] they start to interact laterally, forming sheets with a characteristic intrinsic inward curvature. At a typical number of 13 protofilaments, the tubulin sheet closes into a tube, forming a microtubule. The tubulin lattice has a left-handed helical symmetry. The microtubule closes at the seam (black arrows), where there is a discontinuity point in the helical lattice.
the helical symmetry of microtubule lattice has not yet been clearly explained, it has been speculated that helicity could be a necessary geometrical requirement for the correct self-assembly of microtubules [6]. Microtubules, although often regarded as a load-bearing component of the cytoskeleton, are far from just being static struts. Instead, they are highly dynamical structures, able to switch rapidly between phases of assembly (growth) and disassembly (shrinkage) on the time scale of seconds. Because of this process, the microtubule is said to have an inherent ‘dynamic instability’. This property of microtubules is interesting for bionanotechnology because control over assembly and disassembly of supramolecular architectures is a very active area of research in this field [7]. A discussion on dynamic instability is beyond the scope of this opinion. An excellent overview on microtubule polymerization dynamics is provided, for instance, by Desai and Mitchison [8].
Protofilament architecture and mechanical anisotropy Structural investigations and theoretical calculations show that lateral and longitudinal tubulin interactions have different properties [9–11]. Whereas the lateral inter-PF contacts (a-a, b-b) are mostly electrostatic, the intra-PF (-ab-ab-) interactions are prevalently hydrophobic [11,12]. Interestingly, facilitating lateral association with electrostatic forces and axial self-assembly with the hydrophobic effect is a principle exploited in bionanotechnology for building-up peptide nanoropes [13]. The inter-PF tubulin bonds are weaker (7 kcal/ mol [14]) and more compliant than the longitudinal ones along individual PFs [14,15]. X-ray crystallography and cryo-electron microscopy have shown that the main structural motif involved in inter-PF contacts is the so-called ‘Mloop’ [11,12,15–17] (Figure 2a,b). The M-loop of one tubulin interacts with the H1-S2 loop of the adjacent tubulin (Figure 2a,b) [17]. The N- and C-terminal parts of the
Figure 2. Protofilament–protofilament lateral contacts in microtubules. (a) Protofilaments associate laterally with a 0.9 nm offset. The main structural feature involved in lateral interaction is the M-loop. It establishes contacts with the a-helix H3 and the loops H2-S3/H1-S2 of the neighboring protofilament. (b) Further important lateral interactions are H9/H3 and H10-S9 loop/H4, located at different radial positions with respect to the center of the cross-section. (Tubulin structure: Protein Data Bank entry 1TUB. Molecular graphics images were produced using the UCSF Chimera package from the Resource for Biocomputing, Visualization and Informatics at the University of California, San Francisco, supported by NIH P41 RR-01081).
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Opinion M-loop are considerably flexible and appear to work like a hinge, allowing relative motion between PFs, such as sliding [12]. It has been shown by electron microscopy that PFs slide past each other longitudinally when the microtubule is bent by thermal forces [18,19]. The relative sliding is very tiny ( <0.2 nm), but easily resolved by electron microscopy. Inter-PF bonds are stretched as a consequence of sliding. The resulting lattice tension can be relieved by a twisting of the PF along the microtubule’s axis [5]. The ability to accommodate larger deformations of the inter-PF bonds by PF twisting has important structural consequences because it allows the existence of microtubules with a different number of PFs (from 10 to 16) (Figure 3) [5,19]. Such PF-number polymorphism has physiological significance [20]. The PF structure has also an important effect on microtubule mechanics. The different strengths of intra- and inter-PF bonds imply that the elastic modulus along the microtubule axis is different from the moduli along the axes parallel to the cross-section. Mechanics of microtubules In cells, microtubules are often highly bent because of the action of strong internal cytoskeletal forces [21,22]. Several approaches have been developed to measure the bending stiffness of microtubules. One method is the analysis of thermal shape fluctuations via fluorescence light microscopy [23]. Alternatively, the microtubule bending stiffness has been determined by applying controlled forces. Optical tweezers [24], atomic force microscopes (AFMs) [25,26] or
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hydrodynamic flow [27] have been employed to this purpose. The persistence lengths (Figure 4, Box 1) of microtubules obtained by these techniques fall within the range of 1 to 6 millimeters, implying that they are very stiff on the cell length scale (10 mm). Most of the previous work has modeled microtubules as isotropic tubes with a single Young’s modulus. However, such a simplified picture is inadequate for describing microtubule mechanics [23]. Recent experiments show that the elastic modulus parallel to the microtubule’s axis differs drastically from that of the cross-section or, in other words, microtubules are mechanically strongly anisotropic (Figure 4) [28]. Mechanical anisotropy is found in nearly all macroscopic biological materials, such as bones, wood, stalks, stems and bamboo culms. In most cases, the most stiff direction lies parallel to the long axis [2]. Interestingly, at a completely different length scale, the exact same observations are made for micrometer-sized microtubules. Needleman et al. [29] probed the radial mechanical properties of microtubules by varying the osmotic pressure acting on the microtubule’s wall. They found that the wall deforms from a circular to an elliptic shape above a critical pressure, Pcr = 600 Pa, which is four orders of magnitude smaller than the one predicted by modeling the microtubule as an isotropic tube [29]. Such unexpectedly soft response along the cross-section is likely to be derived from the deformability of inter-PF lateral contacts. The data by Needleman et al. [29] have been successfully explained by an orthotropic elastic shell model for microtubules that accounts for the different contributions of intra- and inter-PF bonds [30]. In a further study, the
Figure 3. Polymorphism of microtubules. (a) Schematic representation of the helical surface lattice of a 3-start 13-protofilament microtubule (modified, with permission, from [18]). Because dimers in adjacent protofilaments are axially shifted (for a 3-start 13-protofilament microtubule the subunit rise is 0.9 nm), the 3-start left-handed helix closes exactly three monomers above its starting point. (b) In a 14-protofilament microtubule, the tubulin dimers at the helix closure are not registered (i). The energetically most favorable way to compensate this mismatch is to skew the protofilaments at a small angle of 0.758 (ii). This produces a left-handed superhelix in the 14-protofilament microtubule with a shallow pitch of 2 mm. (c) Schematic representation of microtubule’s surface for 13, 14 and 16 protofilaments. Notice the skew angle for 14- and 16protofilament microtubules and the left-handedness (14-protofilament microtubule) and right-handedness (16-protofilament microtubule) of the superhelices (blue arrows). The 16-protofilament microtubule has a 4-start helix and no seam. (d) Isosurface rendering of the electron density in a 15-protofilament microtubule. The superhelix is righthanded in 15-protofilament microtubules (blue arrow). The protofilaments’ skew angle and the superhelix’s right-handedness are clearly visible (data from cryo-electron microscopy and helical three-dimensional reconstruction, courtesy of Linda Sandblad, European Molecular Biology Laboratory).
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Figure 4. Anisotropic mechanical properties of microtubules. (a) A flexible polymer bends over relatively short lengths, coiling up on itself. The ‘persistence length’ (Lp) is the length separating bends along the biopolymer contour. The shorter the persistence length compared to the total length (or ‘contour length’), the more flexible is the polymer. The filament in (i) is flexible: Lp is shorter than the contour length. By contrast, the filament in (ii) is stiff: Lp is larger than the contour length. Microtubules have a length up to tens of micrometers and a persistence length in the millimeter range. Thus, microtubules are extremely stiff polymers. (b) Long microtubules are stiffer than shorter ones, which can be shown by plotting the persistence length (Lp) of microtubules against increasing contour length (L). This counter-intuitive behavior is a consequence of bending-associated shear. (c) In a bending microtubule, adjacent tubulins shear (shear strain g1) and stretch the lateral links between protofilaments (i,iii). From electron microscopy studies it is known that stretching of the lateral links is relieved by protofilaments skewing (shear strain g2) (ii,iv) and that protofilament skewing induces a twist in the lattice of the microtubule. This implies that protofilament shearing and twisting are coupled deformations in the microtubule (iii,iv).
dependence of the microtubule’s persistence length on the contour length was investigated by analysing thermal fluctuations of the free tip of grafted microtubule (Figure 4a) [31,32]. The data showed a surprising dependence of the persistence length on the total length (Figure 4b). For total microtubule lengths shorter than 5 mm, the persistence length is on the order of 500 mm [32]. For longer microtubules, the persistence length increases proportionally to L2. A qualitatively similar dependence was also observed in AFM experiments [26]. To model the data in [31] and [26], an additional shear modulus was included in the bending equations. This modulus is a measure for the tendency of elements of the microtubule to slide past each other (Figure 4c) [33,34]. The inter-PF bonds (in the M-loop region) can be identified as the probable shear-bearing elements because they can be easily deformed by thermal fluctuations [18,19]. InterPF sliding releases the elastic energy stored in a bent microtubule, thereby avoiding a structural collapse due to stress concentration in the lattice [2,18,19]. Thus, interPF sliding improves the resiliency of microtubules by preventing the formation of ‘kinks’ and other types of failures under bending stresses. Consequently, microtubules can be bent elastically to small radii of curvature without rupture [22]. For instance, the average radius of curvature of microtubules in a blood platelet is 1 mm [35]. Moreover, buckling microtubules to radii of curvatures <1 mm by using optical tweezers does not result in breaking, even if high curvature is maintained for up to one hour [22]. These examples show microtubules’ remarkable resiliency, which allows the cell to resist damage from the strong contractile forces involved, for example, in cell migration [36]. Microtubules are often not found individually but are arranged in bundles. Bundling is essential for mechanical reinforcement of the cell. The bending stiffness of a bundle can vary by orders of magnitude depending on the strength of cross-linkers between individual filaments. The bending stiffness of a bundle with weak cross-linkers is approximately proportional to the number of filaments, whereas,
in the case of strong cross-linkers, the bending stiffness is approximately proportional to the square of the number of filaments [34]. Thus, bundling allows a ‘fine-tuning’ of the mechanical properties of microtubule-based organelles. Specialized microtubule bundles are involved in chromosome segregation, motility and mechanosensing. Examples of these organelles are the mitotic spindle in dividing cells [37], cilia and flagella [38] and the axostyle in some protists [39]. Parallels with CNTs Considering their remarkable mechanical properties, the question arises of how microtubules and microtubule bundles could be exploited in material science and bionanotechnology. Elegant proof-of-principle experiments have been performed by combining microtubules with microfluidic devices. For example, nanotransport and nanosorting systems have been realized with microtubules traveling on microfluidic lanes coated with the motor protein kinesin [40,41]. Although this approach is extremely promising for laboratory-on-a-chip systems, it does not directly rely on the mechanical properties of microtubules. A further possibility is using microtubules as a template, for example, for the production of structurally defined and monodisperse metallic nanowires [42]. The drawback in this case is that the sophisticated interplay between architecture and mechanics found in microtubules is not preserved in these fully metallic nanoobjects. A third and more viable option would be to apply our understanding of microtubule architecture for the creation of fully synthetic biomimetic nanofibers. Microtubule-inspired nanofibers should be as ‘smart’ as microtubules but chemically stable over a much wider range of environmental conditions. Toward this goal, CNTs are obvious candidates as suitable building blocks. CNTs (Figure 5) are in several aspects the technological counterpart of nature’s microtubules. A side-by-side comparison with microtubules (see also Table 1) could provide useful insights for the fabrication of novel CNTbased nanomaterials. Ideally, such novel materials would 305
Opinion Box 1. Mechanical properties of microtubules Stress Stress is defined as the load per unit area: s = P/A (where s = stress, P = load, A = area). It is expressed in Newton per square meter (N/m2). Strain Strain expresses the deformation of a material under load. A rod with original length L stretched by an amount DL by the action of a stress on it, is subject to a strain e = DL/L. Young’s modulus In linear elasticity theory, it is a constant (E) that expresses the stiffness of a material and is defined as the ratio of stress to strain: E = s/e. Shear The shear stress measures the tangential load per unit area needed to let one part of a material slide past the neighboring part. It is expressed in Newton per square meter (N/m2). The shear strain, g, is angular and measured in radians. In linear elasticity theory, the shear modulus, G (units N/m2), is defined as the ratio between shear stress and shear strain. Bending stiffness A measure of how a certain structure can be deflected under load. The bending stiffness is defined as the bending moment per curvature necessary to bend a filament. For isotropic materials, the bending stiffness, El, is the product of the Young’s modulus, E, and a geometric parameter, l, the momentum of inertia of the cross section. Persistence length Lp – this parameter (used particularly in polymer physics) also defines the bending stiffness of a filament. It is the length along the filament over which the tangent to the contour remains correlated when a filament fluctuates under thermal forces. It is related to the bending stiffness, El, by the relation Lp = El/KBT (where KB = Boltzmann’s constant, T = temperature). Resilience This is the quality of a material to be deflected elastically to small radii of curvature without breaking by storing strain energy. Microtubules are highly resilient but not ‘floppy’. In fact, they have a large Young’s modulus of 2 GPa, but they can be bent to a radius as small as rc = 86 nm in the sporozoite of Plasmodium berghei (a rodent malaria parasite) [68]. This corresponds to a local strain of e 0.14 (e = rMT/rc, where rMT = the microtubule’s radius, rc = the radius of curvature of a bent microtubule) and represents a difference in length of 14% between the two sides. In living fibroblasts, an average bending radius of 0.4 mm was measured on intact microtubules [22]. This corresponds to a length difference of 3% between the two sides. For comparison, elementary calculations show that a hypothetical nylon nanotube of the same scale and comparable Young’s modulus would already have broken apart at a radius of curvature of 2 mm (0.6% difference between the two sides). Carbon nanotubes (CNTs) are also highly resilient. For example, an 850 nm long, 10.5 nm diameter CNT was bent with an atomic force microscope (AFM) to a radius of curvature of 20 nm (corresponding to a local strain e 0.25) repeatedly and without breakage [51].
combine the high mechanical and chemical stability of CNTs with the self-assembling ability and multifunctionality of microtubule structures. Structure and mechanics of CNTs CNTs are members of the structural family of fullerene, an allotropic form of carbon. Single-wall CNTs (SWCNTs) can be essentially considered as two-dimensional graphite 306
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sheets wrapped onto a tube surface [43]. The outer diameter is 1–2 nm, and the wrapping direction determines the possible lattice symmetries (Figure 5a) [44]. Other types of CNTs are multi-walled CNTs (MWCNTs) and carbon nanoropes. Whereas MWCNTs are onion-like arrangements of concentric SWCNTs (Figure 5b), carbon nanoropes are bundles of SWCNTs tightly packed in hexagonal order (Figure 5c,d). The Young’s modulus of individual SWCNTs has been obtained from the amplitude of thermally excited vibrations measured with transmission electron microscopy. An average Young’s modulus of 1.25 TPa (higher than diamond) has been found [45]. The same method has given a modulus of 1.8 TPa for MWCNTs [46]. By laterally deflecting MWCNTs with AFM, a Young’s modulus of 1.3 TPa has been measured [47]. A similar approach applied to individual SWCNTs and SWCNT ropes has given a Young’s modulus of 1 TPa [48,49]. These experiments show that SWCNTs, SWCNT ropes, and MWCNTs are extremely stiff structures. Their high bending stiffness is mainly due to the rigid s-bonds between carbon atoms. However, CNTs are also remarkably resilient. Even after extreme bending to a local strain of e 16%, MWCNTs reversibly come back to their original shape [47,50,51]. This behavior results from the high anisotropy of graphite and the nested structure of MWCNTs [50,52]. Carbon nanoropes are mechanically anisotropic as well [52]. AFM experiments with carbon nanoropes revealed that the low intertube shear stiffness dominates their bending behavior [49]. In fact, the weak Van der Waals interactions (deriving from out-of-plane p-bonds) allow the individual SWCNTs to slide with respect to each other. As for microtubules, the CNT bending properties can be appropriately modeled by inserting the contribution of the shear modulus in the bending equation [48,49]. The high stiffness, high resiliency and low density of CNTs, are extremely promising for the development of materials with superior properties. A dramatic increase of the strength of a nanorope has been achieved by crosslinking SWCNTs with electron beam irradiation. This method could allow the fabrication of macroscopic ribbons, fibers and strands made entirely of CNTs [53]. A layer of upright CNTs (nanotube ‘forests’) has been used to coat micro-fabric fiber cloths and to obtain multifunctional three-dimensional composites [54]. The aforementioned fabrication strategies pave the way for future technological applications of CNTs. However, these approaches do not exploit ‘bottom-up’ molecular self-assembly. This limits the fabrication of structurally well-defined functional nanoarchitectures based on CNTs [55]. Microtubules versus CNTs Although their elastic moduli differ by orders of magnitude, microtubules and CNTs have similar mechanical behaviors. First, both microtubules and CNTs have a tubular structure that ensures structural efficiency. Hollow, thin-walled sections are in general more efficient than solid ones for carrying loads. Circular tubes are more efficient than other shapes under bending loads that are applied from every possible direction. Additionally, hollow sections use less material than solid ones. Therefore, they
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Figure 5. Structure and polymorphism of carbon nanotubes (CNTs). (a) Models of single-walled CNTs (SWCNTs). There are three possible patterns along the circumference of the CNT: ‘armchair’ (i), ‘zigzag’ (ii) and ‘chiral’ (iii). (b) A multi-wall CNT (MWCNT). The inner diameter is 10 nm. (c) Example of an SWCNT rope with defect-free and parallel walls (modified, with permission, from [66]). (d) Example of an SWCNT rope ‘cross-section’ (modified, with permission, from [66]). (e,f) CNTs dissolved in water via surfactants (e) (modified, with permission, from [67]) and peptides (f) (modified, with permission, from [58]). (Structures in Figure 5a produced with CoNTub v1.0. 5-b from http://www.nano-laboratory.com/nanotube-image3.html).
are lighter and more ‘economical’ while resisting the same bending or torsional load [2]. Second, both microtubules and CNTs are exceptionally resilient, that is, they can be bent to a small radius of curvature and are able to restore their original shape without permanent damage. The resilience of microtubules and CNTs originates from their architecture, which allows the dissipation of part of the bending energy through internal rearrangements. In microtubules, the ‘M-loop’ that links single PFs laterally is deformable and can relieve local bending stress by allowing a limited sliding of PFs past each other. MWCNTs and carbon nanoropes exploit a similar mechanism and dissipate bending energy through sliding of neighboring CNTs. The third similarity between microtubules and CNTs is the ability to form large bundles. CNTs form nested structures, such as MWCNTs, and parallel bundles, such as carbon nanoropes. As with microtubules, CNT bundles have improved stiffness and resiliency. Despite numerous similarities in mechanical behavior, a fundamental difference between microtubules and CNTs is that the former are ‘soft’ materials that self-assemble at mild pH and temperature conditions, whereas the latter are typical hard-matter objects that are fabricated by
spinning, layering and further shaping procedures [54]. However, in recent years, strategies have been developed to enable the self-assembly of CNTs in solution. Dispersion of CNTs in water has been obtained by their non-covalent stabilization with surfactants or polymers or by wrapping with oligopeptides [56,57] (Figure 5e-f). Dispersion in liquid media, and particularly water, is critical for the achievement of molecular-level, ‘bottom-up’ assembly of CNTs because it allows the separation of heterogeneous mixtures of CNTs and the controlled association of functionalized CNTs by hydrophobic, electrostatic or covalent bonding [57,58]. Realization of molecular-level assembly of CNTs could open the way to biomimetic nanomaterials. Toward this goal, microtubules can provide useful insights and inspiration. Insights from microtubules for bionanotechnology and nanomedicine Biomimetic approaches are of great interest for the synthesis of nanomaterials because biological architectures often resist large mechanical stresses much better than man-made ones. This phenomenon is likely to be the result of evolution, which has selected structures with high mech307
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Table 1. Comparison between carbon nanotubes and microtubules Synthesis
Linear dimensions
Lattice
Carbon nanotubes Arc discharge Laser ablation Chemical vapor deposition CNT outer diameter: 1–2 nm CNT inside diameter: 0.8–1.6 nm Wall thickness: diameter of a carbon atom Length-to-diameter ratio: 10 3 Hexagonal lattice with ‘armchair’, ‘zigzag’ or ‘chiral’ arrangements of carbon atoms
Microtubules MTs self-assemble at physiological temperature and pH. Guanosine triphosphate (GTP) is required
Structural polymorphism
CNTs are a seamless graphene cylinder CNTs form bundles (ropes) and multi-walled CNTs through Van der Waals interactions
Mechanical properties Young’s modulus: >1 TPa Highly resilient. CNTs can be bent considerably without damage Low shear modulus (in the case of carbon nanoropes) Structural composites Applications and Fibers and fabric functions Catalysts Biomedical applications
Tube diameter: 25 nm PF diameter: 5–6 nm Wall thickness: 5–6 nm Length-to-diameter ratio: 10 3 Tubular bundle of PFs Polarity (plus/minus ends) Tubulin is packed into a helical lattice with 12 nm pitch in the MT wall PFs twist along the MT, forming left- or right-handed superhelixes MTs are a protein cylinder with a seam (13 PF) and without a seam (15 PF) MTs can accommodate different numbers of PFs (from 9 to 18) MTs linked by proteins form bundles Young’s modulus: 2 GPa Highly resilient. MTs can be bent considerably without damage Low shear modulus Essential functions in cells (mitotic spindle, intracellular transport, cell motility)
Abbreviations: CNT, carbon nanotube; MT, microtubule; PF, protofilament.
anical efficiency. Association into bundles is the basic strategy exploited by microtubules for the creation of reinforced structures and sophisticated ‘active nanomaterials’, which are able to exert and sense forces. A promising future perspective could be applying this ‘blueprint’ of microtubules to the design of fibrous nanomaterials consisting of CNT-based building blocks. As mentioned above, controlled molecular self-assembly of CNTs is already possible [58]. Coating CNTs with oligopeptides enables the production of self-assembled composite structures. By varying the factors that influence peptide–peptide interactions (e.g. salt concentration), these structures can assume a wide range of shapes and sizes, such as cylindrical microfibers and flat ribbons [58]. In addition, DNA could be used as an alternative crosslinker [59], as well as synthetic organic molecules [60]. The length and flexibility of these macromolecular linkers can be precisely determined by chemists, and this will allow for control over the final properties of functional bundled architectures. Flexible and long cross-linkers, such as DNA, would produce bundles that are highly resilient under bending deformations. In this case, the bundle’s bending stiffness would be approximately proportional to the number of CNTs. By contrast, stiff and short linkers, such a small organic molecules, would produce more rigid bundles with bending stiffness approximately proportional to the square of the CNT number [34]. Thus, the mechanical properties of CNT bundles could be varied at will through the choice of the cross-linkers. Microtubules could inspire the realization of active CNT nanomaterials in the form of force sensors and transducers. By considering a CNT as a ‘protofilament’, artificial microtubules composed of individual CNTs could be built by choosing appropriate linkers. Such ‘synthetic microtubules’ could be used to replicate microtubule-based 308
mechanosensory organelles, such as cilia in epithelial cells. Cilia sense mechanical stimuli and trigger a cell response. Synthetic mechanosensors inspired by cilia and based on CNTs are conceivable [61]. The creation of nanostructures that are sensitive to mechanical forces could lead to novel responsive drug and gene delivery systems. For example, a drug could be caged inside a synthetic microtubule. The carbon ‘protofilaments’ could be cross-linked by molecules sensitive to bending strains, thereby programming the synthetic microtubules to disassemble beyond a certain bending curvature. Thus, the caged drug could be released if shear forces increase, which occurs, for instance, in a blood vessel at the onset of thrombosis [62]. Sensitivity to bending could be achieved by cross-linking CNTs with short peptides, which are cleavable by proteases. Bending of these synthetic microtubules would expose the target peptide and thus trigger the enzymatic disassembly. A similar mechanism is exploited in the cell for the severing of microtubules. A strongly bent microtubule lattice increases the activity of the microtubule-severing enzyme katanin. Through this mechanism, the enzyme ‘feels’ the curvature of each microtubule and specifically cuts highly bent microtubules, thereby triggering a cellular mechanochemical response [22]. Another possibility is the use of light-sensitive cross-linkers, which could trigger the disassembly of synthetic microtubules upon illumination. This approach presents a promising strategy for photodynamic cancer therapy [63]. Conclusions Microtubules are one of nature’s best examples in terms of dynamic ‘smart materials’. Their primary role in living systems is reflected in their ubiquity and the multitude of functions they fulfil in unicellular as well as higher level
Opinion organisms. They are self-assembling structures with outstanding mechanical properties, which combine high stiffness and high resilience. Microtubule mechanics is strongly determined by the PF architecture. Long-range sliding and twisting of PFs dissipates bending energy efficiently. Moreover, the PF structure and the association with microtubule-associated proteins and molecular motors generate a stunning variety of microtubule-based hierarchical structures, from simple bundles to highly specialized cilia and flagella. Each one of these structures has a distinct functional role in the cell. CNTs, as a nanotechnological counterpart of microtubules, are ideal candidates for realizing biomimetic functional equivalents of microtubules and microtubule-based organelles. One of the major challenges associated with this goal is the unspecific hydrophobic aggregation of CNTs in liquid phase. However, new promising approaches for the selfassembly of CNTs in fluid environments can overcome these problems [58,64]. Understanding the relation between molecular architecture and function in microtubules can provide a wealth of insights and inspiration for material scientists. Mimicking the principles learned from microtubules can move bionanotechnology a step closer toward a next generation of materials with improved mechanical efficiency and a wide range of functional properties. Acknowledgements We thank Katja Taute for providing a critical review of the manuscript and numerous valuable suggestions. We gratefully acknowledge A. Hoenger, A. Kruljac-Letunic, T. Surrey, and Z. Yao for helpful discussions and comments on the manuscript and L. Sandblad for providing cryo-electron microscopy data. We thank the National Science Foundation and the Landesstiftung Baden-Wu¨rttemberg for financial support. F.P. thanks E.H.K Stelzer for support and interesting discussions.
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14 Sept, D. et al. (2003) The physical basis of microtubule structure and stability. Protein Sci. 12, 2257–2261 15 VanBuren, V. et al. (2005) Mechanochemical model of microtubule structure and self-assembly kinetics. Biophys. J. 89, 2911–2926 16 Nogales, E. and Wang, H.W. (2006) Structural mechanisms underlying nucleotide-dependent self-assembly of tubulin and its relatives. Curr. Opin. Struct. Biol. 16, 221–229 17 Li, H. et al. (2002) Microtubule structure at 8 A resolution. Structure 10, 1317–1328 18 Chretien, D. and Fuller, S.D. (2000) Microtubules switch occasionally into unfavorable configurations during elongation. J. Mol. Biol. 298, 663–676 19 Chretien, D. et al. (1998) Limited flexibility of the inter-protofilament bonds in microtubules assembled from pure tubulin. Eur. Biophys. J. 27, 490–500 20 Wade, R.H. et al. (1990) Characterization of microtubule protofilament numbers. How does the surface lattice accommodate? J. Mol. Biol. 212, 775–786 21 Waterman-Storer, C.M. and Salmon, E.D. (1997) Actomyosin-based retrograde flow of microtubules in the lamella of migrating epithelial cells influences microtubule dynamic instability and turnover and is associated with microtubule breakage and treadmilling. J. Cell Biol. 139, 417–434 22 Odde, D.J. et al. (1999) Microtubule bending and breaking in living fibroblast cells. J. Cell Sci. 112, 3283–3288 23 Gittes, F. et al. (1993) Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape. J. Cell Biol. 120, 923–934 24 Felgner, H. et al. (1996) Flexural rigidity of microtubules measured with the use of optical tweezers. J. Cell Sci. 109, 509–516 25 de Pablo, P.J. et al. (2003) Deformation and collapse of microtubules on the nanometer scale. Phys. Rev. Lett. 91, 098101 26 Kis, A. et al. (2002) Nanomechanics of microtubules. Phys. Rev. Lett. 89, 248101 27 Venier, P. et al. (1994) Analysis of microtubule rigidity using hydrodynamic flow and thermal fluctuations. J. Biol. Chem. 269, 13353–13360 28 Tuszynski, J.A. et al. (2005) Anisotropic elastic properties of microtubules. Eur. Phys. J. E. Soft Matter 17, 29–35 29 Needleman, D.J. et al. (2005) Radial compression of microtubules and the mechanism of action of taxol and associated proteins. Biophys. J. 89, 3410–3423 30 Wang, C.Y. et al. (2006) Orthotropic elastic shell model for buckling of microtubules. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 052901 31 Pampaloni, F. et al. (2006) Thermal fluctuations of grafted microtubules provide evidence of a length-dependent persistence length. Proc. Natl. Acad. Sci. U. S. A. 103, 10248–10253 32 Taute, K.M. et al. (2008) Microtubule dynamics depart from the wormlike chain model. Phys. Rev. Lett. 100, 028102 33 Kollar, L.P. and Springer, G.S. (2003) Mechanics of Composite Structures, Cambridge University Press 34 Heussinger, C. et al. (2007) Statistical mechanics of semiflexible bundles of wormlike polymer chains. Phys. Rev. Lett. 99, 048101 35 Bray, D. (2001) Cell Movements: From Molecules to Motility, Garland Publishing 36 Small, J.V. et al. (2002) How do microtubules guide migrating cells? Nat. Rev. Mol. Cell Biol. 3, 957–964 37 Karsenti, E. and Vernos, I. (2001) The mitotic spindle: a self-made machine. Science 294, 543–547 38 Oda, T. et al. (2007) Three-dimensional structures of the flagellar dynein-microtubule complex by cryoelectron microscopy. J. Cell Biol. 177, 243–252 39 Benchimol, M. et al. (2000) The fine structure of the axostyle and its associations with organelles in Trichomonads. Tissue Cell 32, 178–187 40 van den Heuvel, M.G. et al. (2006) Molecular sorting by electrical steering of microtubules in kinesin-coated channels. Science 312, 910–914 41 Ionov, L. et al. (2006) Reversible switching of microtubule motility using thermoresponsive polymer surfaces. Nano Lett. 6, 1982–1987 42 Behrens, S. et al. (2004) Silver nanoparticle and nanowire formation by microtubule templates. Chem. Mater. 16, 3085–3090 43 White, C.T. et al. (1993) Helical and rotational symmetries of nanoscale graphitic tubules. Phys. Rev. B 47, 5485–5488
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44 Qian, D. (2002) Mechanics of carbon nanotubes. Appl. Mech. Rev. 55, 495–532 45 Krishnan, A. et al. (1998) Young’s modulus of single-walled nanotubes. Phys. Rev. B 58, 14013–14019 46 Treacy, M.M.J. et al. (1996) Exceptionally high Young’s modulus observed for individual carbon nanotubes. Nature 381, 678–680 47 Wong, E.W. et al. (1997) Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes. Science 277, 1971– 1975 48 Salvetat, J.P. et al. (1999) Mechanical properties of carbon nanotubes. Appl. Phy. A Mater. Sci. Process. 69, 255–260 49 Salvetat, J.P. et al. (1999) Elastic and shear moduli of single-walled carbon nanotube ropes. Phys. Rev. Lett. 82, 944–947 50 Yu, M.F. (2004) Fundamental mechanical properties of carbon nanotubes: current understanding and the related experimental studies. J. Eng. Mater. Technol. Transact. 126, 271–278 51 Falvo, M.R. et al. (1997) Bending and buckling of carbon nanotubes under large strain. Nature 389, 582–584 52 Lu, J.P. (1997) Elastic properties of carbon nanotubes and nanoropes. Phys. Rev. Lett. 79, 1297–1300 53 Kis, A. et al. (2004) Reinforcement of single-walled carbon nanotube bundles by intertube bridging. Nat. Mater. 3, 153–157 54 Veedu, V.P. et al. (2006) Multifunctional composites using reinforced laminae with carbon-nanotube forests. Nat. Mater. 5, 457–462 55 Balzani, V. et al. (2002) Controlled disassembling of self-assembling systems: toward artificial molecular-level devices and machines. Proc. Natl. Acad. Sci. U. S. A. 99, 4814–4817 56 Lin, Y. et al. (2004) Advances toward bioapplications of carbon nanotubes. J. Mater. Chem. 14, 527–541
57 Zorbas, V. et al. (2004) Preparation and characterization of individual peptide-wrapped single-walled carbon nanotubes. J. Am. Chem. Soc. 126, 7222–7227 58 Dieckmann, G.R. et al. (2003) Controlled assembly of carbon nanotubes by designed amphiphilic Peptide helices. J. Am. Chem. Soc. 125, 1770– 1777 59 Williams, K.A. et al. (2002) Nanotechnology – carbon nanotubes with DNA recognition. Nature 420, 761 60 Sarikaya, M. et al. (2003) Molecular biomimetics: nanotechnology through biology. Nat. Mater. 2, 577–585 61 Malone, A.M. et al. (2007) Primary cilia mediate mechanosensing in bone cells by a calcium-independent mechanism. Proc. Natl. Acad. Sc.i U. S. A. 104, 13325–13330 62 Hathcock, J.J. (2006) Flow effects on coagulation and thrombosis. Arterioscler. Thromb. Vasc. Biol. 26, 1729–1737 63 Shum, P. et al. (2001) Phototriggering of liposomal drug delivery systems. Adv. Drug Deliv. Rev. 53, 273–284 64 Qiao, R. and Ke, P.C. (2006) Lipid-carbon nanotube self-assembly in aqueous solution. J. Am. Chem. Soc. 128, 13656–13657 65 Kuchnir Fygenson, D. et al. (1995) Spontaneous nucleation of microtubules. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 51, 5058–5063 66 Monthioux, M. et al. (2001) Sensitivity of single-wall carbon nanotubes to chemical processing: an electron microscopy investigation. Carbon 39, 1251–1272 67 Islam, M.F. et al. (2003) High weight fraction surfactant solubilization of single-wall carbon nanotubes in water. Nano Lett. 3, 269–273 68 Cyrklaff, M. et al. (2007) Cryoelectron tomography reveals periodic material at the inner side of subpellicular microtubules in apicomplexan parasites. J. Exp. Med. 204, 1281–1287
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Microtubule architecture: inspiration for novel carbon nanotube-based biomimetic materials Francesco Pampaloni1 and Ernst-Ludwig Florin2 1 2
Cell Biology and Biophysics Unit, European Molecular Biology Laboratory, Meyerhofstrasse 1, D-69117 Heidelberg, Germany Center for Nonlinear Dynamics, University of Texas, Austin, TX 78712, USA
Microtubules are self-assembling biological nanotubes that are essential for cell motility, cell division and intracellular trafficking. Microtubules have outstanding mechanical properties, combining high resilience and stiffness. Such a combination allows microtubules to accomplish multiple cellular functions and makes them interesting for material sciences. We review recent experiments that elucidate the relationship between molecular architecture and mechanics in microtubules and examine analogies and differences between microtubules and carbon nanotubes, which are their closest equivalent in nanotechnology. We suggest that a longterm goal in bionanotechnology should be mimicking the properties of microtubules and microtubule bundles to produce new functional nanomaterials. Introduction Microtubules are cytoskeletal biopolymers that, along with actin and intermediate filaments, accomplish essential functions at each stage of the cell’s life cycle. They ensure the mechanical stability of the mitotic spindle, provide oriented tracks for intracellular trafficking of organelles and support the cell’s shape during migration [1]. At the cell length scale, microtubules are very stiff filaments. The average Young’s modulus of a microtubule, considered as a simple isotropic tube, is 2 GPa. Thus, microtubules are as stiff as hard plastic and about one hundred times stiffer than the other cytoskeleton components, actin and intermediate filaments [1]. Interestingly, microtubules are not only stiff, but also highly resilient. Their efficient combination of high stiffness (relative to the other cytoskeletal filaments) and resilience is due to the anisotropic molecular architecture of microtubules and allows them to accomplish multiple tasks in the cell. On the one hand, high stiffness is required to resist the large pushing forces occurring during mitotic spindle elongation at the end of anaphase. On the other hand, high resilience allows microtubules to search the cellular space laterally for binding partners and to keep growing in a different direction without breaking when encountering obstacles. As microtubules are extraordinarily versatile structures, the question arises of what could be learned from them for the design of novel structural and multifunctional Corresponding authors: Pampaloni, F. ([email protected]); Florin, E.-L. ([email protected]).
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materials for applications in material sciences and bionanotechnology. Carbon nanotubes (CNTs), one of the most promising products of nanotechnology, are the closest technological counterpart of microtubules. CNTs are an extremely stiff material; their Young’s modulus is 1 TPa, about five times higher than that of steel (210 GPa) [2]. Similar to microtubules, CNTs are also highly resilient. It is generally acknowledged that CNTs will play a major role in the development of new materials, with applications ranging from ‘super-tough’ composite fibers [3] to drug-delivery systems [4]. Molecular control over the CNT assembly process would be desirable for the full exploitation of their nanoscale properties and for the reproducible fabrication of CNT-based materials. However, although CNTs aggregate into bundles or sheets spontaneously, their assembly into designed composite structures remains difficult to understand and to direct at molecular level. Microtubules and CNTs are surprisingly similar in their mechanical behavior despite their very different chemical composition (proteins and non-covalent interactions in the case of microtubules, carbon and covalent bonds in the case of CNTs) and elastic moduli. Here, we describe key structural aspects of microtubules and review recent results on their mechanics. We then compare CNTs and microtubules side-by-side with respect to structural and elastic properties. Finally, we discuss examples of how microtubules and microtubule-based structures could provide insights for the design and assembly of novel CNT-based biomimetic materials. Structure of microtubules The basic building unit of microtubules is the heterodimeric protein tubulin, consisting of a and b subunits. Tubulin dimers self-assemble head-to-tail (-ab-ab-) into linear protofilaments (PFs) (Figure 1). The cylindrical wall most commonly comprises 13 PFs in vivo, but this number can vary from 9 to 16 in vitro [5]. Tubulins of adjacent PFs are laterally linked through homologous monomer contacts a-a, b-b (except at the ‘seam’, Figure 1). In the microtubule, stacked PFs are slightly longitudinally displaced with respect to each other (0.9 nm in a 13-PF microtubule). This displacement results in a left-handed helical surface lattice. Although the biological function of
0167-7799/$ – see front matter ß 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.tibtech.2008.03.002 Available online 21 April 2008
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Figure 1. Polymerization of microtubules. Tubulin dimers assemble ‘head-to-tail’, forming oligomers that elongate into protofilaments. As the protofilaments reach an estimated critical length of 12 2 dimers [65] they start to interact laterally, forming sheets with a characteristic intrinsic inward curvature. At a typical number of 13 protofilaments, the tubulin sheet closes into a tube, forming a microtubule. The tubulin lattice has a left-handed helical symmetry. The microtubule closes at the seam (black arrows), where there is a discontinuity point in the helical lattice.
the helical symmetry of microtubule lattice has not yet been clearly explained, it has been speculated that helicity could be a necessary geometrical requirement for the correct self-assembly of microtubules [6]. Microtubules, although often regarded as a load-bearing component of the cytoskeleton, are far from just being static struts. Instead, they are highly dynamical structures, able to switch rapidly between phases of assembly (growth) and disassembly (shrinkage) on the time scale of seconds. Because of this process, the microtubule is said to have an inherent ‘dynamic instability’. This property of microtubules is interesting for bionanotechnology because control over assembly and disassembly of supramolecular architectures is a very active area of research in this field [7]. A discussion on dynamic instability is beyond the scope of this opinion. An excellent overview on microtubule polymerization dynamics is provided, for instance, by Desai and Mitchison [8].
Protofilament architecture and mechanical anisotropy Structural investigations and theoretical calculations show that lateral and longitudinal tubulin interactions have different properties [9–11]. Whereas the lateral inter-PF contacts (a-a, b-b) are mostly electrostatic, the intra-PF (-ab-ab-) interactions are prevalently hydrophobic [11,12]. Interestingly, facilitating lateral association with electrostatic forces and axial self-assembly with the hydrophobic effect is a principle exploited in bionanotechnology for building-up peptide nanoropes [13]. The inter-PF tubulin bonds are weaker (7 kcal/ mol [14]) and more compliant than the longitudinal ones along individual PFs [14,15]. X-ray crystallography and cryo-electron microscopy have shown that the main structural motif involved in inter-PF contacts is the so-called ‘Mloop’ [11,12,15–17] (Figure 2a,b). The M-loop of one tubulin interacts with the H1-S2 loop of the adjacent tubulin (Figure 2a,b) [17]. The N- and C-terminal parts of the
Figure 2. Protofilament–protofilament lateral contacts in microtubules. (a) Protofilaments associate laterally with a 0.9 nm offset. The main structural feature involved in lateral interaction is the M-loop. It establishes contacts with the a-helix H3 and the loops H2-S3/H1-S2 of the neighboring protofilament. (b) Further important lateral interactions are H9/H3 and H10-S9 loop/H4, located at different radial positions with respect to the center of the cross-section. (Tubulin structure: Protein Data Bank entry 1TUB. Molecular graphics images were produced using the UCSF Chimera package from the Resource for Biocomputing, Visualization and Informatics at the University of California, San Francisco, supported by NIH P41 RR-01081).
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Opinion M-loop are considerably flexible and appear to work like a hinge, allowing relative motion between PFs, such as sliding [12]. It has been shown by electron microscopy that PFs slide past each other longitudinally when the microtubule is bent by thermal forces [18,19]. The relative sliding is very tiny ( <0.2 nm), but easily resolved by electron microscopy. Inter-PF bonds are stretched as a consequence of sliding. The resulting lattice tension can be relieved by a twisting of the PF along the microtubule’s axis [5]. The ability to accommodate larger deformations of the inter-PF bonds by PF twisting has important structural consequences because it allows the existence of microtubules with a different number of PFs (from 10 to 16) (Figure 3) [5,19]. Such PF-number polymorphism has physiological significance [20]. The PF structure has also an important effect on microtubule mechanics. The different strengths of intra- and inter-PF bonds imply that the elastic modulus along the microtubule axis is different from the moduli along the axes parallel to the cross-section. Mechanics of microtubules In cells, microtubules are often highly bent because of the action of strong internal cytoskeletal forces [21,22]. Several approaches have been developed to measure the bending stiffness of microtubules. One method is the analysis of thermal shape fluctuations via fluorescence light microscopy [23]. Alternatively, the microtubule bending stiffness has been determined by applying controlled forces. Optical tweezers [24], atomic force microscopes (AFMs) [25,26] or
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hydrodynamic flow [27] have been employed to this purpose. The persistence lengths (Figure 4, Box 1) of microtubules obtained by these techniques fall within the range of 1 to 6 millimeters, implying that they are very stiff on the cell length scale (10 mm). Most of the previous work has modeled microtubules as isotropic tubes with a single Young’s modulus. However, such a simplified picture is inadequate for describing microtubule mechanics [23]. Recent experiments show that the elastic modulus parallel to the microtubule’s axis differs drastically from that of the cross-section or, in other words, microtubules are mechanically strongly anisotropic (Figure 4) [28]. Mechanical anisotropy is found in nearly all macroscopic biological materials, such as bones, wood, stalks, stems and bamboo culms. In most cases, the most stiff direction lies parallel to the long axis [2]. Interestingly, at a completely different length scale, the exact same observations are made for micrometer-sized microtubules. Needleman et al. [29] probed the radial mechanical properties of microtubules by varying the osmotic pressure acting on the microtubule’s wall. They found that the wall deforms from a circular to an elliptic shape above a critical pressure, Pcr = 600 Pa, which is four orders of magnitude smaller than the one predicted by modeling the microtubule as an isotropic tube [29]. Such unexpectedly soft response along the cross-section is likely to be derived from the deformability of inter-PF lateral contacts. The data by Needleman et al. [29] have been successfully explained by an orthotropic elastic shell model for microtubules that accounts for the different contributions of intra- and inter-PF bonds [30]. In a further study, the
Figure 3. Polymorphism of microtubules. (a) Schematic representation of the helical surface lattice of a 3-start 13-protofilament microtubule (modified, with permission, from [18]). Because dimers in adjacent protofilaments are axially shifted (for a 3-start 13-protofilament microtubule the subunit rise is 0.9 nm), the 3-start left-handed helix closes exactly three monomers above its starting point. (b) In a 14-protofilament microtubule, the tubulin dimers at the helix closure are not registered (i). The energetically most favorable way to compensate this mismatch is to skew the protofilaments at a small angle of 0.758 (ii). This produces a left-handed superhelix in the 14-protofilament microtubule with a shallow pitch of 2 mm. (c) Schematic representation of microtubule’s surface for 13, 14 and 16 protofilaments. Notice the skew angle for 14- and 16protofilament microtubules and the left-handedness (14-protofilament microtubule) and right-handedness (16-protofilament microtubule) of the superhelices (blue arrows). The 16-protofilament microtubule has a 4-start helix and no seam. (d) Isosurface rendering of the electron density in a 15-protofilament microtubule. The superhelix is righthanded in 15-protofilament microtubules (blue arrow). The protofilaments’ skew angle and the superhelix’s right-handedness are clearly visible (data from cryo-electron microscopy and helical three-dimensional reconstruction, courtesy of Linda Sandblad, European Molecular Biology Laboratory).
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Figure 4. Anisotropic mechanical properties of microtubules. (a) A flexible polymer bends over relatively short lengths, coiling up on itself. The ‘persistence length’ (Lp) is the length separating bends along the biopolymer contour. The shorter the persistence length compared to the total length (or ‘contour length’), the more flexible is the polymer. The filament in (i) is flexible: Lp is shorter than the contour length. By contrast, the filament in (ii) is stiff: Lp is larger than the contour length. Microtubules have a length up to tens of micrometers and a persistence length in the millimeter range. Thus, microtubules are extremely stiff polymers. (b) Long microtubules are stiffer than shorter ones, which can be shown by plotting the persistence length (Lp) of microtubules against increasing contour length (L). This counter-intuitive behavior is a consequence of bending-associated shear. (c) In a bending microtubule, adjacent tubulins shear (shear strain g1) and stretch the lateral links between protofilaments (i,iii). From electron microscopy studies it is known that stretching of the lateral links is relieved by protofilaments skewing (shear strain g2) (ii,iv) and that protofilament skewing induces a twist in the lattice of the microtubule. This implies that protofilament shearing and twisting are coupled deformations in the microtubule (iii,iv).
dependence of the microtubule’s persistence length on the contour length was investigated by analysing thermal fluctuations of the free tip of grafted microtubule (Figure 4a) [31,32]. The data showed a surprising dependence of the persistence length on the total length (Figure 4b). For total microtubule lengths shorter than 5 mm, the persistence length is on the order of 500 mm [32]. For longer microtubules, the persistence length increases proportionally to L2. A qualitatively similar dependence was also observed in AFM experiments [26]. To model the data in [31] and [26], an additional shear modulus was included in the bending equations. This modulus is a measure for the tendency of elements of the microtubule to slide past each other (Figure 4c) [33,34]. The inter-PF bonds (in the M-loop region) can be identified as the probable shear-bearing elements because they can be easily deformed by thermal fluctuations [18,19]. InterPF sliding releases the elastic energy stored in a bent microtubule, thereby avoiding a structural collapse due to stress concentration in the lattice [2,18,19]. Thus, interPF sliding improves the resiliency of microtubules by preventing the formation of ‘kinks’ and other types of failures under bending stresses. Consequently, microtubules can be bent elastically to small radii of curvature without rupture [22]. For instance, the average radius of curvature of microtubules in a blood platelet is 1 mm [35]. Moreover, buckling microtubules to radii of curvatures <1 mm by using optical tweezers does not result in breaking, even if high curvature is maintained for up to one hour [22]. These examples show microtubules’ remarkable resiliency, which allows the cell to resist damage from the strong contractile forces involved, for example, in cell migration [36]. Microtubules are often not found individually but are arranged in bundles. Bundling is essential for mechanical reinforcement of the cell. The bending stiffness of a bundle can vary by orders of magnitude depending on the strength of cross-linkers between individual filaments. The bending stiffness of a bundle with weak cross-linkers is approximately proportional to the number of filaments, whereas,
in the case of strong cross-linkers, the bending stiffness is approximately proportional to the square of the number of filaments [34]. Thus, bundling allows a ‘fine-tuning’ of the mechanical properties of microtubule-based organelles. Specialized microtubule bundles are involved in chromosome segregation, motility and mechanosensing. Examples of these organelles are the mitotic spindle in dividing cells [37], cilia and flagella [38] and the axostyle in some protists [39]. Parallels with CNTs Considering their remarkable mechanical properties, the question arises of how microtubules and microtubule bundles could be exploited in material science and bionanotechnology. Elegant proof-of-principle experiments have been performed by combining microtubules with microfluidic devices. For example, nanotransport and nanosorting systems have been realized with microtubules traveling on microfluidic lanes coated with the motor protein kinesin [40,41]. Although this approach is extremely promising for laboratory-on-a-chip systems, it does not directly rely on the mechanical properties of microtubules. A further possibility is using microtubules as a template, for example, for the production of structurally defined and monodisperse metallic nanowires [42]. The drawback in this case is that the sophisticated interplay between architecture and mechanics found in microtubules is not preserved in these fully metallic nanoobjects. A third and more viable option would be to apply our understanding of microtubule architecture for the creation of fully synthetic biomimetic nanofibers. Microtubule-inspired nanofibers should be as ‘smart’ as microtubules but chemically stable over a much wider range of environmental conditions. Toward this goal, CNTs are obvious candidates as suitable building blocks. CNTs (Figure 5) are in several aspects the technological counterpart of nature’s microtubules. A side-by-side comparison with microtubules (see also Table 1) could provide useful insights for the fabrication of novel CNTbased nanomaterials. Ideally, such novel materials would 305
Opinion Box 1. Mechanical properties of microtubules Stress Stress is defined as the load per unit area: s = P/A (where s = stress, P = load, A = area). It is expressed in Newton per square meter (N/m2). Strain Strain expresses the deformation of a material under load. A rod with original length L stretched by an amount DL by the action of a stress on it, is subject to a strain e = DL/L. Young’s modulus In linear elasticity theory, it is a constant (E) that expresses the stiffness of a material and is defined as the ratio of stress to strain: E = s/e. Shear The shear stress measures the tangential load per unit area needed to let one part of a material slide past the neighboring part. It is expressed in Newton per square meter (N/m2). The shear strain, g, is angular and measured in radians. In linear elasticity theory, the shear modulus, G (units N/m2), is defined as the ratio between shear stress and shear strain. Bending stiffness A measure of how a certain structure can be deflected under load. The bending stiffness is defined as the bending moment per curvature necessary to bend a filament. For isotropic materials, the bending stiffness, El, is the product of the Young’s modulus, E, and a geometric parameter, l, the momentum of inertia of the cross section. Persistence length Lp – this parameter (used particularly in polymer physics) also defines the bending stiffness of a filament. It is the length along the filament over which the tangent to the contour remains correlated when a filament fluctuates under thermal forces. It is related to the bending stiffness, El, by the relation Lp = El/KBT (where KB = Boltzmann’s constant, T = temperature). Resilience This is the quality of a material to be deflected elastically to small radii of curvature without breaking by storing strain energy. Microtubules are highly resilient but not ‘floppy’. In fact, they have a large Young’s modulus of 2 GPa, but they can be bent to a radius as small as rc = 86 nm in the sporozoite of Plasmodium berghei (a rodent malaria parasite) [68]. This corresponds to a local strain of e 0.14 (e = rMT/rc, where rMT = the microtubule’s radius, rc = the radius of curvature of a bent microtubule) and represents a difference in length of 14% between the two sides. In living fibroblasts, an average bending radius of 0.4 mm was measured on intact microtubules [22]. This corresponds to a length difference of 3% between the two sides. For comparison, elementary calculations show that a hypothetical nylon nanotube of the same scale and comparable Young’s modulus would already have broken apart at a radius of curvature of 2 mm (0.6% difference between the two sides). Carbon nanotubes (CNTs) are also highly resilient. For example, an 850 nm long, 10.5 nm diameter CNT was bent with an atomic force microscope (AFM) to a radius of curvature of 20 nm (corresponding to a local strain e 0.25) repeatedly and without breakage [51].
combine the high mechanical and chemical stability of CNTs with the self-assembling ability and multifunctionality of microtubule structures. Structure and mechanics of CNTs CNTs are members of the structural family of fullerene, an allotropic form of carbon. Single-wall CNTs (SWCNTs) can be essentially considered as two-dimensional graphite 306
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sheets wrapped onto a tube surface [43]. The outer diameter is 1–2 nm, and the wrapping direction determines the possible lattice symmetries (Figure 5a) [44]. Other types of CNTs are multi-walled CNTs (MWCNTs) and carbon nanoropes. Whereas MWCNTs are onion-like arrangements of concentric SWCNTs (Figure 5b), carbon nanoropes are bundles of SWCNTs tightly packed in hexagonal order (Figure 5c,d). The Young’s modulus of individual SWCNTs has been obtained from the amplitude of thermally excited vibrations measured with transmission electron microscopy. An average Young’s modulus of 1.25 TPa (higher than diamond) has been found [45]. The same method has given a modulus of 1.8 TPa for MWCNTs [46]. By laterally deflecting MWCNTs with AFM, a Young’s modulus of 1.3 TPa has been measured [47]. A similar approach applied to individual SWCNTs and SWCNT ropes has given a Young’s modulus of 1 TPa [48,49]. These experiments show that SWCNTs, SWCNT ropes, and MWCNTs are extremely stiff structures. Their high bending stiffness is mainly due to the rigid s-bonds between carbon atoms. However, CNTs are also remarkably resilient. Even after extreme bending to a local strain of e 16%, MWCNTs reversibly come back to their original shape [47,50,51]. This behavior results from the high anisotropy of graphite and the nested structure of MWCNTs [50,52]. Carbon nanoropes are mechanically anisotropic as well [52]. AFM experiments with carbon nanoropes revealed that the low intertube shear stiffness dominates their bending behavior [49]. In fact, the weak Van der Waals interactions (deriving from out-of-plane p-bonds) allow the individual SWCNTs to slide with respect to each other. As for microtubules, the CNT bending properties can be appropriately modeled by inserting the contribution of the shear modulus in the bending equation [48,49]. The high stiffness, high resiliency and low density of CNTs, are extremely promising for the development of materials with superior properties. A dramatic increase of the strength of a nanorope has been achieved by crosslinking SWCNTs with electron beam irradiation. This method could allow the fabrication of macroscopic ribbons, fibers and strands made entirely of CNTs [53]. A layer of upright CNTs (nanotube ‘forests’) has been used to coat micro-fabric fiber cloths and to obtain multifunctional three-dimensional composites [54]. The aforementioned fabrication strategies pave the way for future technological applications of CNTs. However, these approaches do not exploit ‘bottom-up’ molecular self-assembly. This limits the fabrication of structurally well-defined functional nanoarchitectures based on CNTs [55]. Microtubules versus CNTs Although their elastic moduli differ by orders of magnitude, microtubules and CNTs have similar mechanical behaviors. First, both microtubules and CNTs have a tubular structure that ensures structural efficiency. Hollow, thin-walled sections are in general more efficient than solid ones for carrying loads. Circular tubes are more efficient than other shapes under bending loads that are applied from every possible direction. Additionally, hollow sections use less material than solid ones. Therefore, they
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Figure 5. Structure and polymorphism of carbon nanotubes (CNTs). (a) Models of single-walled CNTs (SWCNTs). There are three possible patterns along the circumference of the CNT: ‘armchair’ (i), ‘zigzag’ (ii) and ‘chiral’ (iii). (b) A multi-wall CNT (MWCNT). The inner diameter is 10 nm. (c) Example of an SWCNT rope with defect-free and parallel walls (modified, with permission, from [66]). (d) Example of an SWCNT rope ‘cross-section’ (modified, with permission, from [66]). (e,f) CNTs dissolved in water via surfactants (e) (modified, with permission, from [67]) and peptides (f) (modified, with permission, from [58]). (Structures in Figure 5a produced with CoNTub v1.0. 5-b from http://www.nano-laboratory.com/nanotube-image3.html).
are lighter and more ‘economical’ while resisting the same bending or torsional load [2]. Second, both microtubules and CNTs are exceptionally resilient, that is, they can be bent to a small radius of curvature and are able to restore their original shape without permanent damage. The resilience of microtubules and CNTs originates from their architecture, which allows the dissipation of part of the bending energy through internal rearrangements. In microtubules, the ‘M-loop’ that links single PFs laterally is deformable and can relieve local bending stress by allowing a limited sliding of PFs past each other. MWCNTs and carbon nanoropes exploit a similar mechanism and dissipate bending energy through sliding of neighboring CNTs. The third similarity between microtubules and CNTs is the ability to form large bundles. CNTs form nested structures, such as MWCNTs, and parallel bundles, such as carbon nanoropes. As with microtubules, CNT bundles have improved stiffness and resiliency. Despite numerous similarities in mechanical behavior, a fundamental difference between microtubules and CNTs is that the former are ‘soft’ materials that self-assemble at mild pH and temperature conditions, whereas the latter are typical hard-matter objects that are fabricated by
spinning, layering and further shaping procedures [54]. However, in recent years, strategies have been developed to enable the self-assembly of CNTs in solution. Dispersion of CNTs in water has been obtained by their non-covalent stabilization with surfactants or polymers or by wrapping with oligopeptides [56,57] (Figure 5e-f). Dispersion in liquid media, and particularly water, is critical for the achievement of molecular-level, ‘bottom-up’ assembly of CNTs because it allows the separation of heterogeneous mixtures of CNTs and the controlled association of functionalized CNTs by hydrophobic, electrostatic or covalent bonding [57,58]. Realization of molecular-level assembly of CNTs could open the way to biomimetic nanomaterials. Toward this goal, microtubules can provide useful insights and inspiration. Insights from microtubules for bionanotechnology and nanomedicine Biomimetic approaches are of great interest for the synthesis of nanomaterials because biological architectures often resist large mechanical stresses much better than man-made ones. This phenomenon is likely to be the result of evolution, which has selected structures with high mech307
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Table 1. Comparison between carbon nanotubes and microtubules Synthesis
Linear dimensions
Lattice
Carbon nanotubes Arc discharge Laser ablation Chemical vapor deposition CNT outer diameter: 1–2 nm CNT inside diameter: 0.8–1.6 nm Wall thickness: diameter of a carbon atom Length-to-diameter ratio: 10 3 Hexagonal lattice with ‘armchair’, ‘zigzag’ or ‘chiral’ arrangements of carbon atoms
Microtubules MTs self-assemble at physiological temperature and pH. Guanosine triphosphate (GTP) is required
Structural polymorphism
CNTs are a seamless graphene cylinder CNTs form bundles (ropes) and multi-walled CNTs through Van der Waals interactions
Mechanical properties Young’s modulus: >1 TPa Highly resilient. CNTs can be bent considerably without damage Low shear modulus (in the case of carbon nanoropes) Structural composites Applications and Fibers and fabric functions Catalysts Biomedical applications
Tube diameter: 25 nm PF diameter: 5–6 nm Wall thickness: 5–6 nm Length-to-diameter ratio: 10 3 Tubular bundle of PFs Polarity (plus/minus ends) Tubulin is packed into a helical lattice with 12 nm pitch in the MT wall PFs twist along the MT, forming left- or right-handed superhelixes MTs are a protein cylinder with a seam (13 PF) and without a seam (15 PF) MTs can accommodate different numbers of PFs (from 9 to 18) MTs linked by proteins form bundles Young’s modulus: 2 GPa Highly resilient. MTs can be bent considerably without damage Low shear modulus Essential functions in cells (mitotic spindle, intracellular transport, cell motility)
Abbreviations: CNT, carbon nanotube; MT, microtubule; PF, protofilament.
anical efficiency. Association into bundles is the basic strategy exploited by microtubules for the creation of reinforced structures and sophisticated ‘active nanomaterials’, which are able to exert and sense forces. A promising future perspective could be applying this ‘blueprint’ of microtubules to the design of fibrous nanomaterials consisting of CNT-based building blocks. As mentioned above, controlled molecular self-assembly of CNTs is already possible [58]. Coating CNTs with oligopeptides enables the production of self-assembled composite structures. By varying the factors that influence peptide–peptide interactions (e.g. salt concentration), these structures can assume a wide range of shapes and sizes, such as cylindrical microfibers and flat ribbons [58]. In addition, DNA could be used as an alternative crosslinker [59], as well as synthetic organic molecules [60]. The length and flexibility of these macromolecular linkers can be precisely determined by chemists, and this will allow for control over the final properties of functional bundled architectures. Flexible and long cross-linkers, such as DNA, would produce bundles that are highly resilient under bending deformations. In this case, the bundle’s bending stiffness would be approximately proportional to the number of CNTs. By contrast, stiff and short linkers, such a small organic molecules, would produce more rigid bundles with bending stiffness approximately proportional to the square of the CNT number [34]. Thus, the mechanical properties of CNT bundles could be varied at will through the choice of the cross-linkers. Microtubules could inspire the realization of active CNT nanomaterials in the form of force sensors and transducers. By considering a CNT as a ‘protofilament’, artificial microtubules composed of individual CNTs could be built by choosing appropriate linkers. Such ‘synthetic microtubules’ could be used to replicate microtubule-based 308
mechanosensory organelles, such as cilia in epithelial cells. Cilia sense mechanical stimuli and trigger a cell response. Synthetic mechanosensors inspired by cilia and based on CNTs are conceivable [61]. The creation of nanostructures that are sensitive to mechanical forces could lead to novel responsive drug and gene delivery systems. For example, a drug could be caged inside a synthetic microtubule. The carbon ‘protofilaments’ could be cross-linked by molecules sensitive to bending strains, thereby programming the synthetic microtubules to disassemble beyond a certain bending curvature. Thus, the caged drug could be released if shear forces increase, which occurs, for instance, in a blood vessel at the onset of thrombosis [62]. Sensitivity to bending could be achieved by cross-linking CNTs with short peptides, which are cleavable by proteases. Bending of these synthetic microtubules would expose the target peptide and thus trigger the enzymatic disassembly. A similar mechanism is exploited in the cell for the severing of microtubules. A strongly bent microtubule lattice increases the activity of the microtubule-severing enzyme katanin. Through this mechanism, the enzyme ‘feels’ the curvature of each microtubule and specifically cuts highly bent microtubules, thereby triggering a cellular mechanochemical response [22]. Another possibility is the use of light-sensitive cross-linkers, which could trigger the disassembly of synthetic microtubules upon illumination. This approach presents a promising strategy for photodynamic cancer therapy [63]. Conclusions Microtubules are one of nature’s best examples in terms of dynamic ‘smart materials’. Their primary role in living systems is reflected in their ubiquity and the multitude of functions they fulfil in unicellular as well as higher level
Opinion organisms. They are self-assembling structures with outstanding mechanical properties, which combine high stiffness and high resilience. Microtubule mechanics is strongly determined by the PF architecture. Long-range sliding and twisting of PFs dissipates bending energy efficiently. Moreover, the PF structure and the association with microtubule-associated proteins and molecular motors generate a stunning variety of microtubule-based hierarchical structures, from simple bundles to highly specialized cilia and flagella. Each one of these structures has a distinct functional role in the cell. CNTs, as a nanotechnological counterpart of microtubules, are ideal candidates for realizing biomimetic functional equivalents of microtubules and microtubule-based organelles. One of the major challenges associated with this goal is the unspecific hydrophobic aggregation of CNTs in liquid phase. However, new promising approaches for the selfassembly of CNTs in fluid environments can overcome these problems [58,64]. Understanding the relation between molecular architecture and function in microtubules can provide a wealth of insights and inspiration for material scientists. Mimicking the principles learned from microtubules can move bionanotechnology a step closer toward a next generation of materials with improved mechanical efficiency and a wide range of functional properties. Acknowledgements We thank Katja Taute for providing a critical review of the manuscript and numerous valuable suggestions. We gratefully acknowledge A. Hoenger, A. Kruljac-Letunic, T. Surrey, and Z. Yao for helpful discussions and comments on the manuscript and L. Sandblad for providing cryo-electron microscopy data. We thank the National Science Foundation and the Landesstiftung Baden-Wu¨rttemberg for financial support. F.P. thanks E.H.K Stelzer for support and interesting discussions.
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