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doi:10.1016/j.jmb.2003.11.038 J. Mol. Biol. (2004) 335, 1241–1250 Assessing the Flexibility of Intermediate Filaments by Atomic Force Microscopy N. Mücke1†‡, L. Kreplak2†*, R. Kirmse1, T. Wedig3, H. Herrmann3, U. Aebi2 and J. Langowski1 1 Division Biophysics of Macromolecules German Cancer Research Center, 69120 Heidelberg Germany 2 M.E. Müller Institute for Structural Biology Biozentrum, University of Basel, Klingelbergstr. 70 4056 Basel, Switzerland 3 Division Cell Biology German Cancer Research Center, 69120 Heidelberg Germany Eukaryotic cells contain three cytoskeletal filament systems that exhibit very distinct assembly properties, supramolecular architectures, dynamic behaviour and mechanical properties. Microtubules and microfilaments are relatively stiff polar structures whose assembly is modulated by the state of hydrolysis of the bound nucleotide. In contrast, intermediate filaments (IFs) are more flexible apolar structures assembled from a , 45 nm long coiled-coil dimer as the elementary building block. The differences in flexibility that exist among the three filament systems have been described qualitatively by comparing electron micrographs of negatively stained dehydrated filaments and by directly measuring the persistence length of F-actin filaments (, 3 – 10 mm) and microtubules (, 1 – 8 mm) by various physical methods. However, quantitative data on the persistence length of IFs are still missing. Toward this goal, we have carried out atomic force microscopy (AFM) in physiological buffer to characterise the morphology of individual vimentin IFs adsorbed to different solid supports. In addition, we compared these images with those obtained by transmission electron microscopy (TEM) of negatively stained dehydrated filaments. For each support, we could accurately measure the apparent persistence length of the filaments, yielding values ranging between 0.3 mm and 1 mm. Making simple assumptions concerning the adsorption mechanism, we could estimate the persistence length of an IF in a dilute solution to be , 1 mm, indicating that the lower measured values reflect constraints induced by the adsorption process of the filaments on the corresponding support. Based on our knowledge of the structural organisation and mechanical properties of IFs, we reason that the lower persistence length of IFs compared to that of F-actin filaments is caused by the presence of flexible linker regions within the coiled-coil dimer and by postulating the occurrence of axial slipping between dimers within IFs. q 2003 Elsevier Ltd. All rights reserved. *Corresponding author Keywords: statistical analysis; persistence length; surface interaction; electron microscopy; atomic force microscopy Introduction One of the major functions of the cytoskeleton, a complex network of interconnected filaments (i.e. † N.M. and L.K. have contributed equally to this work. ‡ Correspondence concerning the software, e-mail: [email protected] Abbreviations used: IF, intermediate filament; AFM, atomic force microscopy; EM, electron microscopy; HOPG, highly oriented pyrolytic graphite. E-mail address of the corresponding author: [email protected] actin filaments, microtubules, and intermediate filaments), is to determine the shape and mechanical properties of cells. The physical properties of actin filaments and microtubules have been already well characterised at the single filament1,2 and network levels.3,4 In contrast, such knowledge is still sparse for intermediate filaments (IFs) and is urgently needed to understand how diseasecausing inherited mutations in human IF proteins lead to impaired IF assembly and yield an increase in cell fragility in response to mechanical stress.5 – 7 All IF proteins exhibit a characteristic “tripartite” structure which includes an a-helical “rod” 0022-2836/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. 1242 domain flanked by non-a-helical “head” and “tail” domains. The central rod domain contains a pronounced heptad repeat sequence of apolar residues exhibiting the signature of a coiled-coil structure. This periodicity is interrupted by three relatively short variable linkers L1, L12 and L2, leading to four independent a-helical coiled-coil segments, 1A, 1B, 2A and 2B.8 The elementary building block of all IF proteins is a dimer that can, under appropriate buffer conditions,9 selfassemble in vitro into 10 nm wide filaments. For cytoplasmic IFs, an intermediary stable complex is a tetramer comprising two dimers that are arranged in an antiparallel approximately halfstaggered fashion relative to one another. In the case of vertebrate cytoplasmic IFs, the in vitro assembly process follows three distinct steps. First, the tetramers associate laterally into so-called “unit-length” filaments (ULFs). Second, the ULFs anneal longitudinally into filaments of variable width. Third, these filaments compact radially to form smooth-looking IFs 8 –12 nm in diameter (Figure 1).10 The mechanical properties of IF networks in vitro have mainly been studied by rheological and light scattering methods.3,11,12 From these studies it was concluded that individual IFs are relatively flexible polymers and that IF networks exhibit “strain hardening” with a high resistance against rupture. In order to obtain a more quantitative estimate of IF flexibility, human recombinant vimentin was assembled in vitro and the resulting IFs were adsorbed to various solid supports including mica, glass and HOPG (highly oriented pyrolitic graphite). Thus, immobilised filaments were imaged under physiological conditions by atomic force microscopy (AFM), and their contours Vimentin Filament Flexibility were analysed using a statistical polymer chain approach.13,14 Depending on the support used, the apparent persistence length lapp of the vimentin IFs varied from 0.3 mm to 1 mm. The lower value was obtained with mica that interacts strongly with the filaments thereby yielding more compact structures, whereas the upper value was measured on glass that allows the filaments to adopt a contour that is energetically equilibrated to a higher extent in two dimensions. Theory The persistence length l of a filament is a measure of its flexibility and represents a statistical relationship between the contour length s and the end-to-end distance R of a given filament segment. Let us consider a filament of contour length s; which is smoothly bent by an angle Q and energetically equilibrated in two dimensions. The energy necessary to maintain this configuration is given by:15 E ¼ YIQ2 =2s ð1Þ where Y is the Young’s modulus, and I the area moment of inertia of the filament. The persistence length l of the filament can be directly related to these two quantities by:16 YI ¼ kB Tl ð2Þ where kB is the Boltzmann constant and T is the absolute temperature. Using equations (1) and (2), the normalised probability distribution function in two dimensions for a filament bent by an angle Q is Gaussian and can be written as: rffiffiffiffiffiffiffiffiffiffi l 2lQ2 =2s ð3Þ e PðQðsÞÞ2D ¼ 2ps Note that this distribution function depends on the contour length s of the filament. In equation (3), the persistence length l appears as the characteristic length of the distribution. Hence for l q s, the probability of bending the filament is equal to 0 (see also equation (4)). From this distribution, it is possible to compute the mean-square angle and the normalised meanfourth power of the angle: s l ð4Þ ¼3 ð5Þ kQ2 ðsÞl2D ¼ kQ4 ðsÞl2D kQ2 ðsÞl22D Figure 1. Electron micrograph of in vitro assembled recombinant human vimentin intermediate filaments. The bar represents 100 nm. Using equation (3) the mean-square end-to-end distance of a filament of contour length s can also be determined as:17 2l 2 2s=2l 12e kR ðsÞl2D ¼ 4ls 1 2 ð6Þ s Vimentin Filament Flexibility If a filament is energetically equilibrated on a solid support, its persistence length l can be computed from two-dimensional images using equations (4) or (6). In that case and for contour lengths of the filaments in the range of l the value obtained is identical to the persistence length of the same filament in a dilute solution. For contour lengths much larger than l excluded volume effects may apparently stiffen the filaments. If the filament is not equilibrated, the above model only yields an apparent persistence length, which, in turn, depends on the surface adsorption mechanism. Results Contour morphologies of vimentin IFs adsorbed to different solid supports A typical electron micrograph of negatively stained glutaraldehyde-fixed, vimentin filaments exhibits smooth-looking structures approximately 10 nm in diameter (Figure 1). For comparison, Figure 2 displays tapping-mode AFM images in air (Figure 2a) or in physiological buffer (Figure 2b) of vimentin IFs adsorbed to mica, to HOPG (Figure 2c) and to hydrophilic glass (Figure 2d). On all these supports, the filaments appear to be stably attached without the need of any chemical cross-linking. Filaments on mica imaged in air show two different morphologies (Figure 2a) characterised by a height of 0.8 nm and 1.7 nm, respectively, and a full width at half maximum (FWHM) of 100 nm and 45 nm, Figure 2. Tapping mode AFM pictures of in vitro assembled recombinant human vimentin filaments adsorbed on different surfaces. The bar represents 1000 nm. a, Filaments assembled for one hour and imaged in air on mica. b, Filaments assembled for one hour and imaged in liquid on mica. c, Filaments assembled for one hour and imaged in liquid on HOPG. Carbon terraces are clearly visible in the background. d, Filaments assembled for 25 min and imaged in liquid on hydrophilic glass. 1243 respectively. The first type may correspond to filaments that have been spread flattened into protofilaments, whereas the second type may correspond to smooth-looking dried filaments. Notice that in our AFM images no individual protofilamentous substructures could be depicted, contrary to previously described electron micrographs of unravelled filaments.18 In contrast, when imaged in buffer, the filaments adsorbed to the three different supports appear compact and smooth with a height of 3– 5 nm and an apparent diameter of 40– 70 nm. For comparison, neurofilaments exhibit a height of 9.5 nm and a FWHM of 50 nm when covalently bound to a modified glass substrate and imaged by contact mode AFM in buffer.19 However, even if the filaments have a similar height and apparent diameter on the three different supports, they yield very different contours. On mica (Figure 2b), for example, the filaments often show loops in comparison to a more extended appearance of the filaments when adsorbed to HOPG (Figure 2c), hydrophilic glass (Figure 2d), or to carbon-coated copper grids (Figure 1). Such differences in contour are a first hint that the vimentin IFs exhibit somewhat different flexibilities when adsorbed to either mica or to the other three supports. Statistical analysis of IF contours with a 2D equilibration model In order to quantify the apparent flexibility of vimentin IFs after adsorption to the different supports, we used the AFM images to measure the mean-square end-to-end distance kR2 lapp of entire filaments with contour lengths ranging from 2000 nm to 4000 nm (see Table 1). For each filament set, a mean contour length ksl was also computed and used in equation (6) to estimate an apparent persistence length l2kRl (Table 1). As expected from the contour differences observed on the AFM and EM images, the vimentin IFs adsorbed to mica have a lower apparent persistence length (337 nm) than the same filaments adsorbed to HOPG (675 nm), carbon-coated cooper grids (967 nm), or hydrophilic glass (1061 nm). In order to confirm these results and to verify the validity of our statistical model, the angle distribution function Q was estimated as a function of the measured contour length s. For this purpose, the filament contours were divided into sets of segments of fixed contour length s. For each support and a fixed contour length s of 1000 nm, an example of a Q distribution function is displayed in Figure 3a. In each case the distributions could be fitted with similar Gaussian functions, except for mica where the distribution was significantly broader. As stressed when introducing equation (3), the statistical analysis that we have chosen is only valid if the Q distribution function is Gaussian. This property was checked by plotting the normalised mean-fourth power of the angle distribution kQ4 l=kQ2 l2 as a function of the contour 1244 Vimentin Filament Flexibility Table 1. Polymer statistics of IFs adsorbed to different supports Surface kQ4 l=kQ2 l2 l2kQl (nm) kR2 lapp (nm2) ksl (nm) l2kRl (nm) Counts EM grid HOPG Mica Glass 3.08 ^ 0.13 2.30 ^ 0.18 2.73 ^ 0.09 3.02 ^ 0.09 847 769 284 (251a) 980 3.60 £ 106 3.97 £ 106 2.54 £ 106 4.37 £ 106 2266 ^ 409 2626 ^ 669 2545 ^ 495 2497 ^ 458 967 675 337 1061 51 42 57 173 For each support, we have computed the apparent mean-square end-to-end distance kR2 lapp ; the mean contour length ksl; and the normalised mean-fourth power of the angle distribution kQ4 l=kQ2 l2 : The persistence lengths lkR2 l and lkQ2 l were estimated from the experimental end-to-end distances and angle distributions, respectively, using the 2D equilibration model (equations (4) –(6)) described in Theory. All filaments had contour lengths ranging from 2000 nm to 4000 nm. a Linear fit with a non-zero constant, dotted line in Figure 3c. Figure 3. Statistical analysis of filament contours for vimentin IFs adsorbed to hydrophilic glass (black), HOPG (blue), mica (green) and to electron microscopy grids (red). All the filaments had a contour length in the range of 2000 nm to 4000 nm. a, Angle distribution function Q for s ¼ 1000 nm. Continuous lines represent a Gaussian fit of the experimental data. b, Normalised mean-fourth power of the angle distribution kQ4 l=kQ2 l2 as a function of contour length. A value of 3 (straight line) corresponds to a Gaussian distribution function. c, Plot of the mean-square angle kQ2 l as a function of contour length. Each data set is fitted with equation (4) (continuous line) for contour length in the range 600– 1600 nm. For mica, equation (4) does not fit properly and we also show, as a comparison, the result of a linear fit with a non-zero constant (broken line). d, Plot of the mean-square end-to-end distance as a function of the contour length. 1245 Vimentin Filament Flexibility length s (Figure 3b). For contour lengths shorter than 600 nm, some deviation from the theoretical value of 3 (see equation (5)) is observed due to the finite pixel size and the smoothing procedure. Above 600 nm, it was possible to estimate the apparent persistence length lkQ2 l for each support by fitting the behaviour of the mean-square angle kQ2 l as a function of contour length (Figure 3c) with equation (4). The measured apparent persistence lengths lkQ2 l (see Table 1) are 284 nm (mica), 769 nm (HOPG), 847 nm (carbon-coated copper grid), and 980 nm (glass), respectively. These values are consistent with the corresponding l2kRl values (see Table 1 and above). However, it is interesting to note that the linear fits shown in Figure 3c were accurate for the glass and the EM data sets but rather poor for the mica data set and at high contour lengths for the HOPG data set. This clearly indicates that for the first two data sets, the vimentin IFs can effectively be modelled as smoothly bent strings equilibrated in two dimensions. In other words, the influence of the glass and the carbon-coated copper grid on the vimentin IF flexibility is negligible and consequently the apparent persistence length obtained for these two supports, ,1000 nm, should be similar to the persistence length of an unconstrained single vimentin IF in a dilute solution.17,20 In contrast, the filaments adsorbed to mica and HOPG appear more flexible, as indicated by their lower apparent persistence length. For these two supports, a modified version of our statistical model has to be used to analyse the data, i.e. one that takes into account some kind of filamentsupport interaction. The contours of the IFs adsorbed to mica can be described by a quasi-normal projection model Since it is difficult to know the type of interaction that drives the adsorption of vimentin IFs to mica or HOPG, we have decided to use a practical first approximation: if the filament-support interaction is strong enough, a vimentin filament may adsorb to the support as an apparent normal projection of the three-dimensional filament contour onto the plane. Note that the term projection is geometrically incorrect here, since the actual contour length of the filament is conserved upon adsorption. However, by such an approximation the mean-square of the projected end-to-end distance becomes:17 kR2 lproj: ¼ kR2x l þ kR2y l ¼ 2 2 kR l3D 3 ð7Þ For s ! 1: kR2 lproj: ¼ 1 2 kR l2D 3 ð8Þ where kR2 l3D is the mean-square end-to-end distance of the filament equilibrated in a dilute solution, and kR2 l2D is the mean-square end-to-end distance of the filament equilibrated on a solid support (see equation (6)). kR2 l3D and the persistence length l of the filament equilibrated in a dilute solution is given by:14 l 1 2 e2s=l kR2 ðsÞl3D ¼ 2ls 1 2 ð9Þ s To test the validity of the above model, the experimental mean-square end-to-end distance of filaments, with contour lengths ranging between 2000 nm and 4000 nm, was calculated as a function of their contour length s: The corresponding plots are shown in Figure 3d for each support. For s longer than 600 nm, the kR2 l of the filaments adsorbed to mica is smaller and deviates strongly from the kR2 l of the filaments adsorbed to the three other supports. If we assume that the meansquare end-to-end distances measured for the filaments adsorbed to glass or EM grids are a good approximation of kR2 l2D ; the filaments adsorbed to mica are most likely to follow equation (8). As the extrapolation to an infinite contour length of our experimental data is not very reliable, we decided to use another test of the quasi-normal projection model. According to equations (7) and (9), it should be possible to estimate the “true” persistence length of the vimentin IFs equilibrated in a dilute solution from the experimental mean-square end-to-end distance of the filaments adsorbed to mica. The value obtained for l should be similar to that obtained from the glass data set (i.e. ,1000 nm), assuming that the filaments are energetically equilibrated on this support (2D equilibration hypothesis). For this purpose, we determined the persistence length as a function of contour length using the experimental mean-square end-to-end distances of the filaments adsorbed to glass and to mica (Figure 4). For this test, the filaments analysed had contour lengths in the range of 3000 nm to 5500 nm. When the 2D equilibration hypothesis (equation (6)) is used for the mica and glass data sets (Figure 4, diamonds), both curves show an increase of l at low contour length due to the finite pixel size and the smoothing procedure. At high contour length, l is constant and the values obtained for the two data sets are similar to those obtained previously and listed in Table 2, 358 nm for mica and 1107 nm for hydrophilic glass. When the quasi-normal projection hypothesis (equations (7) and (9)) is used for the mica data set (Figure 4, squares), l3D is equal to 1275 nm at high contour length (see Table 2), which is only 15% higher than the value l2D obtained for the glass data set using the 2D equilibration model (1107 nm). However, for filaments with contour lengths below 2500 nm, l is increasing steadily, indicating that the adsorbed filaments cannot be considered as quasi-normal projections any more. In conclusion, for filaments longer than 2500 nm adsorbed to mica, it is possible to calculate with 1246 Vimentin Filament Flexibility HOPG and short filaments (below 2500 nm long; Figure 4) adsorbed to mica, no simple model was able to quantitatively describe the observed behaviours, indicating that the adsorption mechanism is more complex than assumed in these two cases. Discussion The apparent flexibility of vimentin IFs depends on the type of support Figure 4. Apparent persistence length as a function of contour length for hydrophilic glass (black) and mica (green). The apparent persistence length was extracted in two different ways from the mean-square end-to-end distances computed from filaments of contour length in the range of 3000 nm to 5500 nm: diamonds, 2D equilibration model (equation (6)); squares, quasi-normal projection model (equations (7) and (9)). For each curve, the continuous lines are the mean values of the persistence length extracted from the mean-square end-to-end distance obtained by simply taking the entire contour length of the filaments. These values are summarised in Table 2. the quasi-normal projection model a persistence length similar to that obtained by analysing the filaments adsorbed to glass or to EM grids with the 2D equilibration model. Both calculations are confirming that the persistence length of vimentin IFs in a dilute solution is in the range of 1000 nm to 1300 nm. Hence, for such a persistence length, the contour lengths of the adsorbed filaments were always too short to observe any kind of excluded volume effects.17 For the long filaments (above 1400 nm long; Figure 3c) adsorbed to Table 2. Comparison of the two adsorption models Surface Counts ksl (nm) kR2 lapp (nm2) kR2 l3D (nm2) l2D (nm) l3D (nm) Mica Glass 57 3912 ^ 592 4.58 £ 106 6.87 £ 106 358 1275 56 3501 ^ 649 7.72 £ 106 1107 For mica and glass, we have used filaments with contour lengths ranging from 3000 nm to 5500 nm to compute the apparent mean-square end-to-end distance kR2 lapp ; and the mean contour length ksl: As in Table 1 the 2D equilibration model (equation (6)) was used to estimate the persistence length l2D of the filaments adsorbed to each support. For mica only, the quasi-normal projection model was used to estimate kR2 l3D from kR2 lapp (equation (7)). In turn, kR2 l3D was used in combination with ksl in equation (9) to estimate l3D : Vimentin IFs readily adsorb to a wide range of solid supports, with very different surface properties, either being highly negatively charged (mica), hydrophobic (HOPG) or polar (hydrophilic glass). However, on each support the filaments exhibit different flexibilities as emphasised by the broad range of measured apparent persistence lengths (see Figure 2 and Table 1). Similar effects are obtained by varying the adsorption buffer with a given support (data not shown). Such kind of buffer-dependences of the apparent flexibility has been extensively studied by AFM for DNA molecules adsorbed to mica17 and is caused by different kinds of mica – DNA interaction. To our knowledge, this is the first time that a similar effect has been reported with protein filaments. Strikingly, although DNA and vimentin IFs are very different polymers, upon adsorption to a solid support their contours can be accurately described by the linear chain statistics model presented in Theory. With both polymers, depending on the filament-support interaction employed, two principal adsorption scenarios are possible. 1. For an interaction energy in the range of the thermal energy, the filaments will freely equilibrate on the support before they become adsorbed. In this case, the elastic properties are conserved during the adsorption process, so that the measured persistence length is equal to that of a filament equilibrated in a dilute solution. 2. For an interaction energy bigger than the thermal energy, the filaments will be “caught” by the support before having equilibrated so that the filaments are “fixed” into a contour resembling a normal (i.e. perpendicular) projection of the actual three-dimensional contour onto the support. Such a “capture” mechanism yields more condensed filaments on the support and hence a smaller apparent persistence length is revealed. Vimentin IFs equilibrate upon adsorption to glass or to a carbon film (i.e. a glow-discharged carbon-coated EM grid). In contrast, the same filaments appear normally projected when adsorbed to mica. After proper modelling, both data sets yielded a similar estimate of the persistence length l, i.e. 1000 –1300 nm. Strikingly, a similar estimate has been recently derived by Fudge et al. using the 1247 Vimentin Filament Flexibility initial tensile modulus of hagfish slime threads containing mainly keratin-like IFs.21 Concerning the high binding affinity of IFs to different solid supports, it is well known that the nuclear lamins interact with the nuclear surface of the nuclear envelope.22 Similarly, vimentin does associate in vivo with the plasma membrane.23 The lipids composing the plasma membrane have generally polar head groups that may interact with the vimentin IFs in a way similar to the Si – OH groups of the hydrophilic glass. Hence independent of any interaction mediated by membrane proteins, vimentin IFs may in vivo strongly bind to and equilibrate on the plasma membrane, thereby forming a mechanically stable moiety similar to that observed in the eye lens.23 Molecular origin of IF flexibility One would assume that in the case of protein filaments such as, for example, vimentin IFs, a physical parameter like the persistence length should be directly related to their supramolecular architecture and the interactions between neighbouring subunits within the filament. The average vimentin IF cross-section typically contains 16 coiled-coil dimers (, 45 nm long each) that are assumed to be aligned approximately parallel to the filament axis. Depending on the position in the filament, adjacent dimers can be oriented parallel or antiparallel, unstaggered or approximately half-staggered. The lateral interactions between dimers appear relatively strong, since IFs are able to withstand the combined challenge of non-ionic detergents, high salt, ice-cold temperature, and mechanical homogenisation.24 However, during the in vitro assembly process, a distinct tetramer formed by two antiparallel, approximately half-staggered dimers exhibits kinked conformations due to the presence of linkers joining the four different coiled-coil segments, i.e. as emphasised by EM data of vertebrate and invertebrate cytoplasmic IFs.25,26 This molecular flexibility of the tetramers certainly affects the bending rigidity of cytoplasmic IFs. However, it cannot readily explain why the assembly process is very sensitive to variations of pH and temperature thereby yielding totally aberrant filamentous or globular products.9 Cross-linking experiments on hair keratin IFs assembled in vitro under oxidising or reducing conditions have demonstrated that the supramolecular organisation of IFs can be altered by an axial sliding of the constitutive dimers within the filament.27 Small-angle X-ray scattering experiments on stretched hair fibres have documented that such an axial sliding of dimers can also be mechanically induced within a dense array of IFs.28 In fact, a “tetramer switching” mechanism was proposed before, where the two dimers inside a tetramer could slide along each other due to pH or temperature changes, thereby yielding different tetramer types and hence different IF structures.29 In order to get an idea of what can be the effect of this axial sliding mechanism on the flexibility of IFs, we can estimate the persistence length of a filament that would be a one-dimensional liquid of coiled coils implying that there is no significant lateral correlation between the dimers. According to equation (1) the energy necessary to bend such a filament is equal to the number of coiled coils per filament cross-section multiplied by the bending energy of an individual coiled coil. This means that the persistence length of the filament is simply 16 times the persistence length of an individual coiled coil, i.e. 25(^ 15) nm,30 thereby yielding a persistence length l of 400(^ 240) nm, a value roughly two times smaller than our experimentally determined value. Evidently, this estimate is too low, since real IFs are not disordered structures as has been documented by X-ray scattering data of keratin-rich tissues like porcupine quill.31 Taken together, the measured persistence length of vimentin IFs arises from the molecular flexibility of the dimers comprising the filament and from a limited axial sliding of the dimers relative to each other within the filament. However, other hypotheses have been proposed in the literature.21 Comparing the flexibility of IFs and F-actin filaments The basic principles that we used to describe qualitatively the flexibility of IFs should be also valid for other protein filaments such as F-actin filaments and microtubules. The case of F-actin filaments is particularly interesting. Depending on buffer conditions and the presence of binding proteins, they exhibit a persistence length ranging between 3 mm and 10 mm,32,33 which is at least threefold larger than the values measured for vimentin IFs. IFs and F-actin filaments can reach similar lengths and they reveal a similar outer diameter, i.e. 10 nm and 9 nm, respectively. However, the molecular architecture of the two filaments is very different, typically yielding a mass-per-length of , 16 kDa/nm for F-actin filaments34 and , 36 kDa/nm for vimentin IFs.35 Intuitively, since both filaments are protein polymers, we would predict that the filament with the lower mass-per-length, i.e. the F-actin filament, should be more flexible than the vimentin IF. This apparent contradiction may be best explained by analysing the molecular origin of the bending stiffness of F-actin filaments. To a first approximation, F-actin is a two-stranded helical filament built from a 43 kDa globular subunit. The inter-subunit interactions along the two long-pitch helical strands are generally considered stronger than those occurring between the two strands.36 – 38 A priori this particular inter-subunit bonding pattern allows for some lateral slipping between adjacent subunits of the two strands.39 Practically, as the registration between the two strands is fairly well defined, only a small amount of axial slippage occurs. In other words, the two strands forming 1248 the F-actin filament are tightly bound together yielding a higher persistence length than the one measured for vimentin IFs. As for IFs, the amount of axial molecular motion that can take place without disrupting the molecular architecture appears to be the key factor governing the flexibility of F-actin filaments. Following this basic principle, the effect of cations, drugs or interacting proteins on the flexibility of IFs and F-actin filaments could be readily understood.33 Biological significance of IF flexibility? Not only do actin filaments and microtubules serve as “tracks” for molecular motors to move cargoes, but they are also responsible for the dynamic properties of the cytoskeleton which, in turn, determine cell plasticity and drive cell motility and remodelling of cell shape. In contrast, the cytoplasmic IF network is generally considered as a relatively inert and mechanically resistant scaffold.40 This picture appears somehow contradictory, since IFs are more flexible than F-actin filaments and microtubules, as elaborated here. The molecular origin of this flexibility, i.e. a high potential for axial sliding of the dimers relative to one another within the filament, may qualify cytoplasmic IFs as mechanical signal transducers.41 In this context, cells and tissues exhibit a wide spectrum of responses to mechanical stimuli like, for example, shear stress. This indicates that a mechanical signal may be transduced, i.e. via the IF network, from the plasma membrane to the nucleus where a specific response is triggered.42,43 Based on immunofluorescence studies of epithelial cells, keratin IF bundles, i.e. tonofibrils, have been implicated in the transmission of mechanical forces throughout the cytoplasm.44,45 These tonofibrils also reveal wave-like patterns or kinks that can propagate along their length in synchrony with phosphorylation/dephosphorylation cycles.46 This spatial propagation of a distinct filament deformation pattern along the length of an IF bundle is in agreement with our in vitro model of vimentin IF flexibility involving an axial sliding of dimers relative to one another. Ideally this sliding process can proceed all along the length of the filament in a very effective manner, i.e. without disrupting its molecular architecture. In contrast, the rigidity and inter-subunit coupling of F-actin filaments is such that a local deformation is only propagated over a few subunits before it is “fading out” or even reversed.39 Materials and Methods Recombinant vimentin Human vimentin was expressed and purified as described.47 The protein was stored at 2 80 8C in 8 M urea, 5 mM Tris – HCl (pH 7.5), 1 mM DTT, 1 mM EDTA, 0.1 mM EGTA, 10 mM methyl ammonium chloride. The Vimentin Filament Flexibility day before use, the protein was dialysed into 2 mM sodium phosphate (pH 7.5), 1 mM DTT, at room temperature by lowering the urea concentration in a stepwise fashion (6 M, 4 M, 2 M, 0 M). Dialysis was continued overnight at 4 8C into fresh buffer without urea. The next day the protein was dialysed for one hour at 4 8C into 2 mM sodium phosphate (pH 7.5). Filament assembly was performed by adding an equal volume of 200 mM KCl in 2 mM sodium phosphate (pH 7.5) to a 0.4 mg/ml vimentin solution, at 37 8C. After 20 minutes to one hour, the filament solution was diluted 1:80 to 1:300 in 2 mM sodium phosphate (pH 7.5), 100 mM KCl, and 30 ml aliquots were allowed to adsorb to a solid support for at least five minutes prior to AFM imaging. Surface preparation Three kinds of solid supports were used in this study: Muscovite mica, highly oriented pyrolytic graphite (HOPG), and hydrophilic glass. Mica and HOPG were freshly cleaved immediately before use. To obtain a hydrophilic glass surface, we used the following protocol. Standard light microscopy cover slips were washed with ethanol and water, and then exposed for one hour to “Piranha solution”, a mixture of three parts H2SO4 (97%) and one part H2O2 (30%). Next, the cover slips were rinsed in water, exposed twice to ultrasound waves (50 kHz) for ten minutes, and finally dried under a stream of nitrogen. After such treatment, the surface is covered by Si– OH groups that are stable for a few hours. The supports were mounted for AFM imaging in two different ways, both of which proved equally suited. Either, a small piece of support was glued onto a Teflon disc by water-insoluble epoxy glue (Araldit; Ciba-Geigy, Basel, Switzerland). The Teflon disc was then glued (cyanoacrylate glue) to a steel disc and mounted onto the piezoelectric scanner. Or alternatively, a large piece of support was directly glued to a steel disc. Electron microscopy For electron microscopy (EM), filament assembly was terminated after 20 minutes to one hour by the addition of an equal volume of stop buffer (0.2% (w/v) glutaraldehyde in 100 mM KCl, 2 mM sodium phosphate, pH 7.5). After three to five minutes, 5 ml aliquots were adsorbed for one minute to glow-discharged carboncoated copper grids and negatively stained with 2% (w/ v) uranyl acetate for visualisation using a Zeiss 900 transmission electron microscope (Carl Zeiss, Oberkochen, Germany). For image processing, prints enlarged five times from the original negative (50,000 £ ) were digitised. Atomic force microscopy For scanning in air the sample was prepared by the following protocol: 20 ml of assembled vimentin IFs diluted to 0.5 – 2 mg/ml were adsorbed for ten minutes to a freshly cleaved piece of mica. The mica was then washed carefully with 500 ml of assembly buffer (2 mM sodium phosphate (pH 7.5), 100 mM KCl) to remove all non-bound filaments. Next, the filaments attached to the mica were incubated for ten minutes with 100 ml glutaraldehyde (0.5% in 2 mM sodium phosphate, pH 7.5) to stabilise their structure before they were washed with 1249 Vimentin Filament Flexibility 2 ml distilled water and dried under a steady stream of nitrogen. For operating in air we used 125 mm long silicon cantilevers (type NCH from Nanosensors, Neuchâtel, Switzerland), which had a nominal spring constant of 21 – 78 N/m. The cantilever drive frequency was chosen between 200 kHz and 300 kHz, and the scanner drive frequency was fixed to 3 Hz. For scanning in liquid the sample was prepared by adsorbing 20 ml of assembled vimentin IFs, diluted to 0.5– 2 mg/ml, for five minutes to the different solid supports described above. We used 100 mm long cantilevers with oxide sharpened silicon nitride tips, which had a nominal spring constant of 0.38 N/m (type NP-S from Digital Instruments, Santa Barbara, USA). The cantilever drive frequency was chosen between 7.5 kHz and 9.5 kHz, and the scanner drive frequency was fixed to 2 Hz. All AFM images were recorded in tapping-mode using a Nanoscope IIIa running with software version 5.12r3 (Digital instruments, Santa Barbara, USA), operated at room temperature. 512 £ 512 pixels images were recorded at a scan size of either 10 mm or 20 mm, thus resulting in pixel sizes of 20 nm or 40 nm, respectively. For further image processing, 10 mm size zooms were extracted from the 20 mm scans using the Nanoscope III software. AFM images were processed using the ImageJ software. ImageJ is a version of the NIH-Image software developed by the National Institutes of Health. It is a public domain software†. Filament contours were traced and exported as XY-coordinate sets by using either the “Freehand Linetool” or a skeleton algorithm implemented in Image J. Data analysis The XY-coordinate sets of the filament contours were analysed using Thetascan 1.0 developed by N. Mücke in Origin 7.0. To assess the influence of pixel number and the errors introduced by the freehand tracing of the filament contours, computer-generated filaments were first pixelised and their contours traced in the same way as done with the experimental data. It was found that the experimental data acquisition errors can be minimised by a smoothing procedure using the weight average of five contiguous XY-coordinates centred about a given XY-coordinate: Vi;correct ¼ 1Vi22 þ 2Vi21 þ 4Vi þ 2Viþ1 þ 1Viþ2 10 ð10Þ where Vi is the vector of the tangent to the curve on XY-coordinate i: Note that this procedure removes two points at each end of the filament. Next, the corrected XY-coordinate sets of the filament contours were split into segments of increasing contour length in 100 nm increments.20 For each segment set of contour length s, the mean-square angle kQ2 l; the normalised mean-fourth power of the angle kQ4 l=kQ2 l2 and the mean-square end-to-end distance kR2 l were computed. † http://rsb.info.nih.gov/ij Acknowledgements We thank S. Stoll for discussions and support concerning the data analysis software, and J. Spatz for discussions concerning the glass modification protocol. L.K. was supported by a fellowship awarded by the “Fondation pour la Recherche Médicale”. The work was funded by a grant awarded to H.H. by Deutsche Forschungsgemeinschaft (DFG, HE1853/4-1), an NCCR program grant on “Nanoscale Science” awarded to U.A. by the Swiss National Science Foundation, The M.E. Müller Foundation of Switzerland, and the Canton Basel Stadt. References 1. Kis, A., Kasas, S., Babic, B., Kulik, A. J., Benoit, W., Briggs, G. A. et al. (2002). Nanomechanics of microtubules. Phys. Rev. Letters, 89, 248101. 2. Liu, X. & Pollack, G. H. (2002). Mechanics of f-actin characterized with microfabricated cantilevers. Biophys. J. 83, 2705– 2715. 3. Janmey, P. A., Euteneuer, U., Traub, P. & Schliwa, M. (1991). Viscoelastic properties of vimentin compared with other filamentous biopolymer networks. J. Cell Biol. 1, 155– 160. 4. Palmer, A., Xu, J., Kuo, S. C. & Wirtz, D. (1999). Diffusing wave spectroscopy microrheology of actin filament networks. Biophys. J. 76, 1063– 1071. 5. Bonifas, J. M., Rothman, A. L. & Epstein, E. H., Jr (1991). Epidermolysis bullosa simplex: evidence in two families for keratin gene abnormalities. Science, 254, 1202– 1205. 6. Parry, D. A. D. & Steinert, P. M. (1995). IF pathology: molecular consequences of rod and end domain mutations. In Intermediate Filament Structure (Parry, D. A. D. & Steinert, P. M., eds), Springer, Austin. 7. Herrmann, H., Wedig, T., Porter, R. M., Lane, E. B. & Aebi, U. (2002). Characterization of early assembly intermediates of recombinant human keratins. J. Struct. Biol. 137, 82 – 96. 8. Strelkov, S. V., Herrmann, H. & Aebi, U. (2003). Molecular architecture of intermediate filaments. Bioessays, 25, 243– 251. 9. Herrmann, H. & Aebi, U. (1999). Intermediate filament assembly: temperature sensitivity and polymorphism. Cell Mol. Life Sci. 55, 1416– 1431. 10. Herrmann, H. & Aebi, U. (1998). Intermediate filament assembly: fibrillogenesis is driven by decisive dimer – dimer interactions. Curr. Opin. Struct. Biol. 8, 177 –185. 11. Ma, L., Xu, J., Coulombe, P. A. & Wirtz, D. (1999). Keratin filament suspensions show unique micromechanical properties. J. Biol. Chem. 274, 19145–19151. 12. Hohenadl, M., Storz, T., Kirpal, H., Kroy, K. & Merkel, R. (1999). Desmin filaments studied by quasi-elastic light scattering. Biophys. J. 77, 2199–2209. 13. Kratky, O. & Porod, G. (1949). Röntgenuntersuchung aufgelöster Fadenmoleküle. Recueil, 68, 1106–1122. 14. Flory, P. J. (1969). Statistical Mechanics of Chain Molecules, Interscience Publishers, New York. 15. Landau, L. D. & Lifshitz, E. M. (1986). Theory of Elasticity, Pergamon Press, Oxford, NY. 16. Landau, L. D. & Lifshitz, E. M. (1980). Statistical Physics, Part 1, 3rd edit., Pergamon Press, Oxford, NY. 17. Rivetti, C., Guthold, M. & Bustamante, C. (1996). Scanning force microscopy of DNA deposited onto 1250 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. Vimentin Filament Flexibility mica: equilibration versus kinetic trapping studied by statistical polymer chain analysis. J. Mol. Biol. 264, 919– 932. Aebi, U., Fowler, W. E., Rew, P. & Sun, T.-T. (1983). The fibrillar structure of keratin filaments unraveled. J. Cell Biol. 97, 1131– 1143. Karrasch, S., Heins, S., Aebi, U. & Engel, A. (1994). Exploring intermediate filament structure with the scanning forcee microscope: comparison with transmission electron microscopy data. J. Vac. Sci. Technol. B, 12, 1474– 1477. Frontali, C., Dore, E., Ferrauto, A. & Gratton, E. (1979). An absolute method for the determination of the persistence length of native DNA from electron micrographs. Biopolymers, 18, 1353– 1373. Fudge, D. S., Gardner, K. H., Forsyth, V. T., Riekel, C. & Gosline, J. M. (2003). The mechanical properties of hydrated intermediate filaments: insights from hagfish slime threads. Biophys. J. 85, 2015– 2027. Stuurman, N., Heins, S. & Aebi, U. (1998). Nuclear lamins: their structure, assembly, and interactions. J. Struct. Biol. 122, 42 – 66. Ramaekers, F. C., Dunia, I., Dodemont, H. J., Benedetti, E. L. & Bloemendal, H. (1982). Lenticular intermediate-sized filaments: biosynthesis and interaction with plasma membrane. Proc. Natl Acad. Sci. USA, 79, 3208– 3212. Starger, J., Brown, W. E., Goldman, A. E. & Goldman, R. D. (1978). Biochemical and immunological analysis of rapidly purified 10 nm filaments from baby hamster kidney (BHK-21) cells. J. Cell Biol. 78, 93–109. Herrmann, H., Häner, M., Brettel, M., Müller, S. A., Goldie, K. N., Fedtke, B. et al. (1996). Structure and assembly properties of the intermediate filament protein vimentin: the role of its head, rod and tail domains. J. Mol. Biol. 264, 933–953. Geisler, N., Schunemann, J., Weber, K., Haner, M. & Aebi, U. (1998). Assembly and architecture of invertebrate cytoplasmic intermediate filaments reconcile features of vertebrate cytoplasmic and nuclear lamin-type intermediate filaments. J. Mol. Biol. 282, 601– 617. Wang, H., Parry, D. A., Jones, L. N., Idler, W. W., Marekov, L. N. & Steinert, P. M. (2000). In vitro assembly and structure of trichocyte keratin intermediate filaments. A novel role for stabilization by disulfide bonding. J. Cell Biol. 151, 1459– 1468. Kreplak, L., Franbourg, A., Briki, F., Leroy, F., Dallé, D. & Doucet, J. (2002). A new deformation model of hard alpha-keratin fibres at the nanometer scale. Implications for hard alpha-keratin intermediate filament mechanical properties. Biophys. J. 82, 2265–2274. Aebi, U., Häner, M., Troncoso, J., Eichner, R. & Engel, A. (1988). Unifying principles in intermediate filament (IF) structure and assembly. Protoplasma, 145, 73 – 81. Schwaiger, I., Sattler, C., Hostetter, D. R. & Rief, M. (2002). The myosin coiled-coil is a truly elastic protein structure. Nature Mater. 1, 232– 235. Fraser, R. D. B., MacRae, T. P. & Suzuki, E. (1976). Structure of the alpha-keratin microfibril. J. Mol. Biol. 108, 435– 452. 32. Isambert, H., Venier, P., Maggs, A. C., Fattoum, A., Kassab, R., Pantaloni, D. & Carlier, M. F. (1995). Flexibility of actin filaments derived from thermal fluctuations. Effect of bound nucleotide, phalloidin, and muscle regulatory proteins. J. Biol. Chem. 270, 11437– 11444. 33. Steinmetz, M. O., Goldie, K. N. & Aebi, U. (1997). A correlative analysis of actin filament assembly, structure, and dynamics. J. Cell Biol. 138, 559– 574. 34. Steinmetz, M. O., Stoffler, D., Muller, S. A., Jahn, W., Wolpensinger, B., Goldie, K. N. et al. (1998). Evaluating atomic models of F-actin with an undecagoldtagged phalloidin derivative. J. Mol. Biol. 276, 1 – 6. 35. Herrmann, H., Haner, M., Brettel, M., Ku, N. O. & Aebi, U. (1999). Characterization of distinct early assembly units of different intermediate filament proteins. J. Mol. Biol. 286, 1403–1420. 36. Aebi, U., Millonig, R. C., Salvo, H. & Engel, A. (1986). The three-dimensional structure of the actin filament revisited. Ann. N. Y. Acad. Sci. 483, 100– 119. 37. Erickson, H. P. (1989). Co-operativity in protein – protein association. The structure and stability of the actin filament. J. Mol. Biol. 206, 465– 474. 38. Bremer, A., Henn, C., Goldie, K. N., Engel, A., Smith, P. R. & Aebi, U. (1994). Towards atomic interpretation of F-actin filament three-dimensional reconstructions. J. Mol. Biol. 742, 683– 700. 39. Bremer, A., Millonig, R. C., Sütterlin, R., Engel, A., Pollard, T. D. & Aebi, U. (1991). The structural basis for the intrinsic disorder of the actin filament: the “lateral slipping” model. J. Cell Biol. 115, 689– 703. 40. Fuchs, E. & Cleveland, D. W. (1998). A structural scaffolding of intermediate filaments in health and disease. Science, 279, 514– 519. 41. Maniotis, A. J., Chen, C. S. & Ingber, D. E. (1997). Demonstration of mechanical connections between integrins, cytoskeletal filaments, and nucleoplasm that stabilize nuclear structure. Proc. Natl Acad. Sci. USA, 94, 849– 854. 42. Lockard, V. G. & Bloom, S. (1993). Trans-cellular desmin-lamin B intermediate filament network in cardiac myocytes. J. Mol. Cell Cardiol. 25, 303– 309. 43. Bloom, S., Lockard, V. G. & Bloom, M. (1996). Intermediate filament-mediated stretch-induced changes in chromatin: a hypothesis for growth initiation in cardiac myocytes. J. Mol. Cell Cardiol. 28, 2123– 2127. 44. Helmke, B. P., Thakker, D. B., Goldman, R. D. & Davies, P. F. (2001). Spatiotemporal analysis of flowinduced intermediate filament displacement in living endothelial cells. Biophys. J. 80, 184– 194. 45. Helmke, B. P., Rosen, A. B. & Davies, P. F. (2003). Mapping mechanical strain of an endogenous cytoskeletal network in living endothelial cells. Biophys. J. 84, 2691–2699. 46. Yoon, K. H., Yoon, M., Moir, R. D., Khuon, S., Flitney, F. W. & Goldman, R. D. (2001). Insights into the dynamic properties of keratin intermediate filaments in living epithelial cells. J. Cell Biol. 153, 503– 516. 47. Herrmann, H., Hofmann, I. & Franke, W. W. (1992). Identification of a nonapeptide motif in the vimentin head domain involved in intermediate filament assembly. J. Mol. Biol. 223, 637– 650. Edited by M. Moody (Received 30 July 2003; received in revised form 19 November 2003; accepted 19 November 2003)