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Temperature-Dependent Elasticity of Microtubules A. Kis,†,⊥ S. Kasas,‡,§ A. J. Kulik,† S. Catsicas,‡ and L. Forro´*,† Institut de la Physique de la Matie`re Complexe, EPFL, CH-1015 Lausanne, Switzerland, Laboratoire de Neurobiologie Cellulaire, EPFL, CH-1015 Lausanne, Switzerland, and De´partement de Biologie Cellulaire et de Morphologie, UniVersite´ de Lausanne, CH-1015 Lausanne, Switzerland ReceiVed July 18, 2007. ReVised Manuscript ReceiVed March 11, 2008 Central to the biological function of microtubules is their ability to modify their length which occurs by addition and removal of subunits at the ends of the polymer, both in vivo and in vitro. This dynamic behavior is strongly influenced by temperature. Here, we show that the lateral interaction between tubulin subunits forming microtubule is strongly temperature dependent. Microtubules deposited on prefabricated substrates were deformed in an atomic force microscope during imaging, in two different experimental geometries. Microtubules were modeled as anisotropic, with the Young’s modulus corresponding to the resistance of protofilaments to stretching and the shear modulus describing the weak interaction between the protofilaments. Measurements involving radial compression of microtubules deposited on flat mica confirm that microtubule elasticity depends on the temperature. Bending measurements performed on microtubules deposited on lithographically fabricated substrates show that this temperature dependence is due to changing shear modulus, implying that the lateral interaction between the protofilaments is strongly determined by the temperature. These measurements are in good agreement with previously reported measurements of the disassembly rate of microtubules, demonstrating that the mechanical and dynamic properties of microtubules are closely related.
Introduction Along with actin and intermediate filaments, microtubules build the cytoskeleton, the supporting dynamic structure of eukaryotic cells. Inside living cells, microtubules form networks and carry out several vital functions: they act as tracks for the movement of motor proteins and provide mechanical support for the cellular structure. During cell division, part of the microtubule network is reorganized in the form of the miotic spindle which pulls apart chromosomes. This makes microtubules the prime target of several anticancer therapies. Microtubules also form actuating structures such as cilia and flagella that move some eukaryotic and sperm cells. All these functions are largely influenced by their mechanical properties. Quantifying these properties will provide better understanding of various biological processes in which MTs are involved. The basic building block of microtubules is the Rβ-tubulin dimer,1 associating head-to-tail to form a linear chain, the protofilament. Protofilaments bind laterally, forming a hollow cylinder with a typical diameter of 25 nm. In the most usual case, microtubules are composed of 13 protofilaments. Structural studies based on cryo transmission electron microscopy (cryoTEM)2,3 show that the protofilaments are composed of seamlessly connected, indistinguishable tubulin molecules. Neighboring protofilaments are separated by deep grooves, with 10 Å diameter holes in the microtubule’s surface, with very limited dimer segments3 participating in the lateral interaction (Figure 1a). This large discrepancy between contact areas in lateral and longitudinal directions implies a high degree of mechanical anisotropy (parts b and c of Figure 1). * E-mail:
[email protected]. † Institut de la Physique de la Matie`re Complexe. ‡ Laboratoire de Neurobiologie Cellulaire. § De´partement de Biologie Cellulaire et de Morphologie. ⊥ Present address: Laboratory of Nanoscale Electronics and Structures, EPFL, CH-1015 Lausanne. (1) Nogales, E.; Wolf, S. G.; Downing, K. H. Nature 1998, 391, 199–203. (2) Nogales, E.; Whittaker, M.; Milligan, R.; Downing, K. Cell 1999, 96, 79–88. (3) Meurer-Grob, P.; Kasparian, J.; Wade, R. H. Biochemistry 2001, 40, 8000– 8008.
Figure 1. (a) Ribbon diagrams of two tubulin dimers from neighboring protofilaments in a microtubule, viewed along the MT longitudinal axis. Segments of molecules participating in the lateral interaction between the protofilaments (M-loop and H3 R-helix 3) are highlighted in red. (b) Three-dimensional representation of a microtubule. (c) Anisotropic mechanical model of a microtubule used in this work. EYoungdetermines longitudinal “stretchiness” of the microtubule and shear modulus G the lateral interaction between the protofilaments.
Previous measurements of the mechanical properties of microtubules involved deforming microtubules under controlled forces produced by means of optical tweezers,4 hydrodynamic (4) Kurachi, M.; Hoshi, M.; Tashiro, M. Cell Motil. Cytoskeleton 1995, 30, 221–228.
10.1021/la800438q CCC: $40.75 2008 American Chemical Society Published on Web 05/22/2008
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flow,5 and atomic force microscopy (AFM).6–8 An alternative approach employed statistical analysis of thermally induced shape fluctuations.9,10 The physical quantity governing the behavior of microtubules under such mechanical deformation is their resistance to bending, i.e., their flexural rigidity. Until now, microtubules were mostly modeled as elastic, isotropic beams. In this case, the flexural rigidity can be expressed via the Young’s modulus EYoung and the second moment of the cross-sectional area I as EYoungI. Reported values of the Young’s modulus resulting from modeling microtubules as isotropic cylinders spanned a range between 1 MPa6 and 7 GPa.4 However, surface reconstructions of microtubules2,3 show that microtubules are far from smooth, isotropic cylinders and that tubulin subunits are more strongly bound in the longitudinal direction, along the protofilaments than in the lateral direction, between adjacent protofilaments. Bending deformations therefore occur not only by elongation and compression of protofilaments, governed by the Young’s modulus but also by deformation of the lateral contact area between the protofilaments, which can be described as sliding between the protofilaments and is determined by the shear modulus G (Figure 1c). Consequently, the flexural rigidity is no longer given as EYoungI but as EbendingI instead, where the bending modulus Ebending depends both on EYoung and G. In addition, the bending modulus is also length-dependent: bending over large deformation lengths involves less sliding than bending short microtubules. In addition to our previously published work,7 the fact that microtubules have a length dependent mechanical behavior was later confirmed by Pampaloni et al.11 On the basis of this intuitive argument, Ebending approaches the Young’s modulus for long deformation lengths where the microtubule behaves as an isotropic cylinder. For short deformation lengths, the microtubule behaves as a bundle of loosely connected protofilaments, and Ebending closely corresponds to the shear modulus G. Therefore, in order to adequately describe mechanical behavior of microtubules, both EYoung and G have to be determined. Variations of the shear modulus G could provide insight into the interaction between the protofilaments which is important for understanding the dynamic instability. Changes in EYoung could explain mechanical behavior of microtubules on length-scales associated with cells. Our previously published work7 demonstrated that the Ebending of a microtubule deposited on a single pore in Al2O3 shows a 3-fold variation in the 5-42 °C temperature range. However, to fully describe the temperature-dependent elasticity of microtubules as a first step in understanding its molecular origin, one has to deconvolute the temperature variations in EYoung and G. In this study, we present temperature-dependent measurements of microtubule elasticity in two complementary geometries. Microtubules deposited on flat surfaces of mica sheets were elastically deformed in the radial direction. In addition, we have investigated the temperature dependence of the shear modulus G using the previously introduced method for the measurement
Microtubule Assembly. Commercially available bovine brain tubulin (Cytoskeleton, Inc.), purified to 99%, was dissolved in PEM buffer (80 mM Na-PIPES (piperazine-N,N′-bis(2-ethanesulfonic acid)), 1 mM MgCl2, 1 mM EGTA (ethylene glycol-bis(b-aminoethyl ether)-N,N,N′,N′-tetraacetic acid), pH 6.9), with 10% glycerol and 1 mM GTP (guanosine 5′-triphosphate). The final concentration of tubulin was 5 mg/ml. Microtubule assembly was initiated by heating the solution to 37 °C and monitored by measuring the UV absorbance at 350 nm using a spectrophotometer.12 After 20 min, the assembly was blocked by adding glutaraldehyde to a final concentration of 0.5%. Glutaraldehyde fixation was stopped after 1 min by the addition of 150 µl of Tris buffer (100 mM tris(hydroxymethyl)-aminomethane hydrochloride in water) with pH 6.9. This preparation step was necessary for stabilizing microtubules during long experiments and for promoting substrate adhesion. Other potential methods of microtubule stabilization like MAPs (microtubule associated proteins) or taxol (taxoterre) did not result in microtubules that would adhere strongly to the substrate. The short exposure time and concentration result in minimal change in microtubules’ fine structure, as demonstrated in studies of microtubules using video-enhanced DIC (differential interference contrast) microscopy,13 observation of kinesin movement on glutaraldehyde treated microtubules,14 and negligible conformational changes as demonstrated by limited nucleotide release upon glutaraldehyde fixation.15 Glutaraldehyde-fixed microtubules are therefore expected to show qualitative behavior similar to taxol-stabilized microtubules. The solution was centrifuged during 10 min at 6000g in order to separate polymerized microtubules from unpolymerized tubulin. The supernatant containing tubulin was discarded and the pellet resuspended and diluted 20-fold in a buffer having the same composition as the one used for polymerization but without glycerol and GTP. A drop of solution (10 µL) was deposited on the substrate and rinsed with the buffer after 10 s. The surface was never allowed to dry. Substrate Preparation. Microtubules were immobilized on two different kinds of surfaces: (3-aminopropyl)-triethoxysilane (APTES)modified mica and poly(methyl methacrylate) (PMMA) covered with gold. Mica was chemically modified using the vapor transfer technique.16 A small quantity (30 µL) of APTES was placed on the bottom of a 2-L glass desiccator. Freshly cleaved pieces of muscovite mica were placed close to the desiccator’s top, which was then evacuated and purged with argon. The reaction was allowed to proceed for 2 h, resulting in a positively charged, amino-group terminated surface. At the pH of 6.9, the surface of microtubules is negatively charged17 and therefore electrostatically attracted to the positively charged substrate. The starting point for the second type of substrates used in this study was silicon spin-coated with a 400 nm thick layer of PMMA. Slits with widths varying between 80-170 nm were cut into PMMA using electron-beam lithography.7 A 20 nm thick gold layer was thermally evaporated onto the PMMA surface. Good adhesion between the gold and microtubules was assured by the presence of sulfur from the amino acid cysteine on the outer surface of
(5) Venier, P.; Maggs, A. C.; Carlier, M.-F.; Pantaloni, D. J. Biol. Chem. 1994, 269, 13353–13360. (6) Vinckier, A.; Dumortier, C.; Engelborghs, Y.; Hellemans, L. J. Vac. Sci. Technol. B 1996, 14, 1427–1431. (7) Kis, A.; Kasas, S.; Babic, B.; Kulik, A. J.; Benoıˆt, W.; Briggs, G. A. D.; Scho¨nenberger, C.; Catsicas, S.; Forro´, L. Phys. ReV. Lett. 2002, 89, 248101. (8) Pablo, P. J. D.; Schaap, I. A. T.; MacKintosh, F. C.; Schmidt, C. F. Phys. ReV. Lett. 2003, 91, 098101. (9) Mizushima-Sugano, J.; Maeda, T.; Miki-Noumura, T. Biochim. Biophys. Acta 1983, 755, 257–262. (10) Gittes, F.; Mickey, B.; Nettleton, J.; Howard, J. J. Cell Biol. 1993, 120, 923–934. (11) Pampaloni, F.; Lattanzi, G.; Jonas, A.; Surrey, T.; Frey, E.; Florin, E.-L. PNAS 2006, 103, 10248–10253.
(12) Gaskin, F.; Cantor, C. R.; Shelanski, M. J. Mol. Biol. 1974, 89, 737. (13) Cross, A. R.; Williams, R. C. Cell Motil. Cytoskeleton 1991, 20, 272– 278. (14) Turner, D.; Chang, C.; Fang, K.; Cuomo, P.; Murphy, D. Anal. Biochem. 1996, 242, 20–25. (15) Himes, R. H.; Jordan, M. A.; Wilson, L. Cell Biol. Int. Rep. 1982, 6, 697–704. (16) Lyubchenko, Y. L.; Lindsay, S. M., DNA, RNA and Nucleoprotein Complexes Immobilized on AP-mica and Imaged with AFM. In Procedures in Scanning Probe Microscopies; Colton, R. J., Engel, A., Frommer, J. E., Gaub, H. E., Gewirth, A. A., Guckenberger, R., Rabe, J., Heckl, W. M., Parkinson, B., Eds.; John Wiley & Sons Ltd.: Chichester, 1998; pp 493-495. (17) Baker, N. A.; Sept, D.; Holst, M. J.; McCammon, A. J. IBM J. Res. DeV. 2001, 45, 427–438.
of Young’s and shear moduli employing a lithographically tailored substrate containing slits with varying widths.7
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Kis et al. and c of Figure 2) and fitted using the Hertz model for the indentation of a cylinder by a sphere. Neglecting deformation of the silicon-nitride AFM tip, the indentation δ under a normal force F can be expressed by21
[
δ ) C(RMT, Rtip)
]
1 - ν2 F Eradial
2⁄3
and
C(RMT, Rtip) ) K(k′)
(
)( )
A + B 3k RE(k′) 2π
2⁄3
(1)
with Eradial being the radial compressive modulus and ν the Poisson’s ratio. The geometric factor C is given by
A)
1 , Rtip
B)
1 1 1 1 + , , ) 2R R Rtip RMT
k′ ) √1 - k2 (2)
The numerical constant k, determined by the radii Rtip and RMT is the solution of equation
B (1 ⁄ k2)E(k′) - K(k′) ) A K(k′) - E(k′)
(3)
where K(k) and E(k) are elliptic integrals
K(k) )
∫0π⁄2 √1 - k2 sin2 θ dθ,
E(k) )
∫0π⁄2 Microtubule’s height can be expressed as Figure 2. (a) AFM image of a microtubule deposited on APTESfunctionalized mica. (b) Schematic drawing of the compression experiment. Microtubules are deformed in the radial direction during regular contact-mode AFM imaging. The observed deformation is fitted using the Hertz model for the indentation of a cylindrical shell by a sphere, eq 5. (c) Linescans acquired along the white line in part a show microtubule’s height, under two different loading forces.
microtubules.1,18 Sulfur and gold form an essentially covalent bond, with a breaking strength of 1.4 nN,19 far above the typical imaging force of 0.2 nN. Instrumentation. Microtubules were imaged in the liquid environment (PEM buffer) using a commercial AFM (Autoprobe M5 from TermoMicroscopes). Contact-mode imaging was performed using sharpened silicon-nitride microlevers without the metallic coating (Microlevers type C from Veeco), with a nominal spring constant of 0.01 N/m, calibrated by measuring their resonant frequency in air.20 Immersion in liquid or temperature variation used in this study has negligible influence on the cantilever’s spring constant. Temperature was controlled using a Peltier-element based temperature control stage (Molecular Imaging). The sample was placed in a copper liquid container, which was chosen in order to minimize convective currents inside the buffer due to local temperature differences. This setup resulted in temperature stability better than 0.1 °C/hour. Measurements of the Radial Compressive Modulus. The radial deformation of microtubules on flat surfaces was measured by taking a series of contact mode AFM images like the one in Figure 2a, under varying forces. Microtubules were deposited on the surface of APTES-functionalized mica. The indentation of a microtubule was recorded as a change in height due to AFM imaging (parts b (18) Li, H.; DeRosier, D. J.; Nicholson, W. V.; Nogales, E.; Downing, K. H. Structure 2002, 10, 1317–1328. (19) Grandbois, M.; Beyer, M.; Rief, M.; Clausen-Schaumann, H.; Gaub, H. E. Science 1999, 283, 1727–1730. (20) Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. ReV. Sci. Instrum. 1993, 64, 403–405.
[
h ) h0 - C(RMT, Rtip)
1
√1 - k2 sin2 θ
]
1 - ν2 (F + F0) Eradial nominal
dθ (4)
2⁄3
(5)
where h0 corresponds to the height (diameter) of a microtubule without mechanical deformation and is equal to 25 nm.22 The total force F is not necessarily equal to the contact-mode set point: it can contain contributions coming from the interaction between the AFM tip and the microtubule as well as between the microtubule and the substrate. The total force F is therefore written as the sum of the force set point (Fnominal) and a free parameter F0 determined from the fit. The Poisson’s ratio of microtubules is unknown. Choosing the maximal possible value of ν ) 0.5,23 characteristic of rubber, gives the upper estimate of Eradial. The tip radius was estimated from AFM images to be 60 nm, yielding a geometric factor of C ) 302 m1/3. The final result is not very sensitive to the tip radius: a radius of 100 nm would correspond with C ) 290 m1/3. Measurements of the Shear Modulus. Microtubules deposited on gold-coated PMMA surfaces were deformed during AFM imaging in contact mode. This deformation was recoded as local height in the corresponding AFM image (Figure 3a). MTs firmly adhered to the surface due to covalent bonding between cysteine and the gold surface, occasionally spanning holes. The deformation of microtubules on the suspended part (Figure 3b) was modeled using the clamped-beam formula for the deformation of beams under a point load in the middle.23 Structural data2,3 show that microtubules consist of compact protofilaments separated by deep grooves. During mechanical deformation, these thin connections between protofilaments act as “weak links”. Total mechanical deformation is therefore given as the sum of deformation due to the stretching of filaments, determined by EYoungand shearing between the protofilaments, governed by G (21) Boresi, A. P.; Sidebottom, O. M. AdVanced Mechanics of Materials; John Wiley & Sons: New York, 1985; pp 693-702. (22) Chretien, D.; Wade, R. H. Biol. Cell 1991, 71, 161–174. (23) Gere, J. M.; Timoshenko, S. P. Mechanics of materials, 3rd ed.; PWSKent: Boston, 1984; p 690.
Temperature-Dependent Elasticity of Microtubules
δ ) δbending + δshearing )
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FL FL3 FL3 + fs ) 192EYoungI 4GA 192EbendingI (6)
where fs is a shape factor, L is the suspended length, A the crosssectional area, and I the second moment of the cross section, equal to D4/64 for a solid cylinder of diameter D. The deflection length L is directly measured from AFM images. Ebending is the effective, bending modulus introduced to facilitate comparison between results. Its value is equal to the Young’s modulus only when the influence of shearing can be neglected (long microtubules). In that case, the second term in eq 6 coming from shearing can be neglected. Taking into account that microtubules have external and internal diameters Dext and Dint of 25 and 15 nm, respectively (corresponding with 13 protofilament microtubules), eq 6 can be simplified as
1 Ebending
)
1 EYoung
+
2 2 1 3fs(Dext + Dint) G L2
(7)
with the shape factor fs of 1.38.23 EYoung and G can be extrapolated from the mechanical response by varying the suspended length L, using tailored substrates in the form of lithographically patterned PMMA.
Results and Discussion Radial Compression of Microtubules. The height of microtubules on contact-mode AFM images is systematically lower than their diameter inferred from TEM images22 due to mechanical compression provoked by the AFM tip. This compression can be exploited by imaging microtubules under controlled forces. After a suitable microtubule has been found, a series of contactmode AFM images was taken under increasing force set-points. Every image corresponded to the appearance of the surface (and the tube) under a given normal load. Compared to the often-used practice of acquiring force-distance curves on predetermined locations between the acquisition of two AFM images, our approach ensured that the deformation was always recorded at the point of interest, for example, in the middle of the tube. As the applied force increases, microtubule’s height, recorded in the topographic image (Figure 2a), decreases (parts b and c of Figure 2). Fitting the height variation (Figure 4) to the Hertz model (5) gives a value of Eradial ) 17 GPa for the radial compressive modulus. This value corresponds to the upper limit, because of the choice of highest possible Poisson’s ratio i.e., ν ) 0.5. The parameter F0 (eq 5) varied between -1.4 nN and -2.6 nN, with no significant temperature-dependent trend. During indentation, most of the deformation occurs in the area connecting the protofilaments. Measurements of the Young’s modulus, corresponding to the “stretchiness” of protofilaments and shear modulus, describing sliding between the protofilaments show that the shear modulus is at least 2 orders of magnitude lower than Young’s. We can therefore assume that the radial compressive modulus Eradial ) 17 GPa, having the same order of magnitude as Ebending, is much more influenced by the low value of the shear modulus G than the Young’s modulus. The temperature dependence of the radial compressive modulus Eradial, Figure 5, shows a decrease of compliance on lower temperatures, the same qualitative behavior as the one previously published for Ebending.7 Shear Modulus of Microtubules. To separate the contributions of protofilament stretching and shearing between the protofilaments, measurements have to be carried out on microtubules with varying suspended lengths. This was achieved using a lithographically prepared substrate, coated with gold to ensure microtubule adhesion.
Figure 3. (a) Pseudo-3D rendering based on the AFM image of a microtubule deposited on a lithographically tailored substrate with slits of varying widths. The suspended lengths are (from left to right): 178, 170, 148, and 113 nm. Mechanical measurements on these prefabricated surfaces allow simultaneous determination of Young’s and shear moduli. (b) Schematic drawing of the bending experiment. A microtubule deposited on a porous substrate is deformed by the AFM tip during contact-mode imaging. The deflection at the midpoint of the suspended part is extracted from AFM images like the one in part a and fitted using the clamped beam formula, eq 6.
Figure 4. Variation of microtubule’s height for different force set points (nominal force). The microtubule is adsorbed on a flat mica surface and deformed in the radial direction. Data is fitted using the Hertz model, eq 5, yielding the radial compressive modulus Eradial. This measurement was performed at room temperature (20 °C).
Tubes adhere to the surface due to covalent binding between cysteine and gold, occasionally spanning holes, Figure 3a. Microtubules that were selected for measurements did not move over the surface during the experiment. Under loading forces used in this experiment, deformations were observed only on suspended segments of microtubules. Radial deformation of the microtubule was neglected, since no significant change in their height on the supported part could be observed while the force was varied. Previously presented measurements of the radial compressive modulus have shown that a force of 0.2 nN provokes a radial deformation on the order of 1 nm. The deformation of the suspended part was linear within the experimental error. Furthermore, the deformation was reversible,
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Figure 5. Temperature dependence of the radial compressive modulus Eradial of a microtubule. The temperature was varied in the 5-37 °C temperature range. Microtubules are highly anisotropic from the mechanical point of view. The radial compressive modulus Eradialtherefore reflects the temperature sensitivity of weak lateral interaction between neighboring protofilaments. Temperature variation of the bending modulus Ebending in the same temperature range is shown in the inset.
with loading and unloading curves having the same slope and the microtubule recovering the initial shape after the mechanical measurement. To ensure that the measurements were carried out in the elastic regime of microtubule deformation, the imaging force was kept below 0.2 nN in subsequent bending experiments. Under these imaging forces, the microtubule behaved as a linearly elastic material, justifying the choice of eq 6. The fact that microtubules behave as clamped beams was experimentally supported by the observation that AFM imaging in the direction perpendicular to the microtubules’ local shape did not displace them in the lateral direction. The choice of boundary conditions was further verified using finite element analysis,24 which provided numeric proof of the fact that microtubules are firmly clamped at slit edges by comparing shapes of loading curves for different boundary conditions. Measurements of the shear modulus were performed on two temperatures, 37 and 7 °C, Figure 6, corresponding to compliant and rigid states of the microtubule, as seen from previously reported measurements of the bending modulus.7 In the representation chosen in Figure 6, the shear modulus is proportional to the inverse slope of the fit, while the Young’s modulus is the inverse of the segment on the abscissa. Data is fitted to eq 7. The slope clearly decreases when the temperature is decreased, indicating an increase of the shear modulus from G ) 1.9 ( 0.6 MPa at 37 °C to G ) 12 ( 7 MPa at 7 °C. This implies a strong temperature dependence of the lateral interaction between the protofilaments. Previous detailed studies of the dynamic behavior of single microtubules conducted using videoenhanced DIC (differential microscopy) revealed that both the growing and shrinking velocities of microtubules increase by roughly an order of magnitude in this temperature range,25,26 indicating that the dynamic and mechanical properties of microtubules are closely related. Biological Implications. Microtubules are highly dynamic structures, characterized by macroscopic and erratic fluctuations (24) Kasas, S.; Kis, A.; Riederer, B. M.; Forro´, L.; Dietler, G. Chem. Phys. Chem. 2004, 5, 252–257. (25) Fygenson, D. K.; Braun, E.; Libchaber, A. Phys. ReV. E 1994, 50, 1579– 1588. (26) Fygenson, D. K. Microtubules: The Rhythm of Assembly and the Evolution of Form. PhD thesis, Princeton University, Princeton, NJ, 1995.
Kis et al.
Figure 6. Variation of Ebending as a function of suspended length for the microtubule deposited on a lithographically tailored PMMA surface at two different temperatures. Microtubules are more compliant at 37 °C due to a low value of the shear modulus (G ) 1.9 ( 0.6 MPa). A temperature decrease to 7 °C leads an increase of the shear modulus to G ) 12 ( 7 MPa.
in length. If we followed the same microtubule over a certain period of time and under constant conditions we could see its length grow with a fairly constant velocity (∼1µm/s) then suddenly start to shrink (with rate ∼10µm/s). Growing and shrinking occurs by addition and removal of subunits at the ends of the polymer, both in vivo and in vitro.25–28 Transition to shrinking is referred to as catastrophe. Shrinking can suddenly be reversed and the microtubule can start to grow again following a rescue event. The equilibrium concentration of microtubules in a given solution is given by the delicate balance between growing and shrinking rates as well as frequencies of catastrophe and rescue events. The aspects of microtubule dynamics depend on factors like the concentration of monomers, Mg2+ or Ca2+ ions, GTP, temperature, presence of MAPs, etc. In the case of microtubules assembled from mammalian tubulin, the steady state with the highest proportion of microtubules is attained around 37 °C.29 Both the growth and shrinking rates are highest at 37 °C, while they monotonically decrease as the temperature is decreased.25,26 The reason why the equilibrium between tubulin and microtubules shifts toward tubulin at low temperatures is not due to the temperature behavior of assembly and disassembly speeds but mostly to the temperature behavior of rescue and catastrophe events. For mammalian tubulin, at 4 °C there are no rescue events, while the probability of rescue is close to 1 at 37 °C.25,26 Cryo-TEM studies of microtubules show that the distinguishing feature of shrinking microtubule are individual, coiled protofilaments at their ends, lending them a frayed appearance.30 This indicates that “unzipping” of protofilaments at the ends of microtubules plays a significant role in microtubule disassembly. Lateral interaction between protofilaments could therefore be helpful in understanding the disassembly and dynamic instability of microtubules in general. Consequently, measurements of microtubule elasticity on short length scales could be relevant to explaining the dynamic instability of microtubules. (27) Horio, T.; Hotani, H. Nature 1986, 321, 605–607. (28) Wade, R. H.; Hyman, A. A. Curr. Opin. Cell Biol. 1997, 9, 12–17. (29) Olmsted, J. B.; Borisy, G. G. Biochemistry 1975, 14, 2996–3005. (30) Mandelkow, E. M.; Mandelkow, E.; Milligan, R. A. J. Cell Biol. 1991, 114, 977–991.
Temperature-Dependent Elasticity of Microtubules
Conclusion Mechanical measurements presented in this paper show a strong dependence of microtubule rigidity on temperature. The increase of microtubule rigidity as the temperature is lowered from 37 to 5 °C can be completely explained by an increase in the strength of lateral contacts between the protofilaments. The strength of lateral interaction between the protofilaments and its temperature dependence could provide an insight into some of the aspects related to the temperature dependence of microtubule disassembly. The increase in lateral interaction that we observe as the temperature is consistent with previously published measurements that show slowing down of microtubule disassembly with decreasing temperature.25,26 This indicates that mechanical properties, more specifically lateral interaction between the protofilaments, could play a significant role in modulating the dynamic behavior of microtubules. One interesting example for this would be microtubules in organisms living in extreme temperatures, such as arctic fishes. In this case, mutations attributed to increased stability of microtubules at low temper-
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atures are actually localized in the regions responsible for lateral interaction between the protofilaments.32 Future mechanical measurements under various chemical agents and environmental factors that influence microtubule dynamics could yield valuable new insights. On possibility would be to measure the mechanical properties of microtubules as a function of varying pH. Acknowledgment. We thank B. Babic´ and Ch. Scho¨nenberger for preparing lithographically patterned PMMA substrates. We also thank J.-P. Aime´, H.-B. Riederer, and G.A.D. Briggs for inspiring discussions, C. Cibert, G. Dietler, and P. D. L. Rios for their constructive suggestions, and W. Benoıˆt for support. LA800438Q (31) Keskin, O.; Durell, S. R.; Bahar, I.; Jernigan, R. L.; Covell, D. G. Biophys. J. 2002, 83, 663–680. (32) Detrich, H. W.; Parker, S. K.; Williams, R. C., Jr.; Nogales, E.; Downing, K. H. J. Biol. Chem. 2000, 275, 37038–37047. (33) Kasas, S.; Cibert, C.; Kis, A.; De Los Rios, P.; Riederer, B. M.; Forro, L.; Dietler, G.; Catsicas, S. Biol. Cell 2004, 96, 697–700.
