Download Assessing the Flexibility of Intermediate Filaments by Atomic Force

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)