Article No. jmbi.1998.2466 available online at http://www.idealibrary.com on
J. Mol. Biol. (1999) 286, 553±561
Single Molecule Force Spectroscopy of Spectrin
Repeats: Low Unfolding Forces in Helix Bundles
Matthias Rief1,2, Jaime Pascual3, Matti Saraste3 and Hermann E. Gaub1*
1
Lehrstuhl fuÈr angewandte
Physik, Ludwig-Maximilians
UniversitaÈt MuÈnchen
Amalienstrasse 54
D-80799 MuÈnchen, Germany
2
Department of Biochemistry
B405, Stanford University
School of Medicine, Stanford
CA 94305-5307, USA
3
EMBL, Meyerhofstrasse 1
D-69012 Heidelberg, Germany
Spectrin repeats fold into triple helical coiled-coils comprising 106
amino acid residues. Using an AFM-related technique we measured the
force required to mechanically unfold these repeats to be 25 to 35 pN.
Under tension, individual spectrin repeats unfold independently and in
an all-or-none process. The dependence of the unfolding forces on the
pulling speed reveals that the corresponding unfolding potential is shallow with an estimated width of 1.5 nm. When the unfolded polypeptide
strand is relaxed, several domains refold within less than a second. The
unfolding forces of the a-helical spectrin domains are ®ve to ten times
lower than those found in domains with b-fold, like immunoglobulin or
®bronectin Ill domains, where the tertiary structure is stabilized by
hydrogen bonds between adjacent strands. This shows that the forces
stabilizing the coiled-coil lead to a mechanically much weaker structure
than multiple hydrogen-bonded b-sheets.
# 1999 Academic Press
*Corresponding author
Keywords: spectrin; unfolding forces; protein folding; AFM; force
spectroscopy
Introduction
Recent advances in picoNewton instrumentation
have made it possible to perform mechanical
experiments with single molecules (Kishino &
Yanagida, 1988; Rief et al., 1997b; Smith et al.,
1992). This has given experimental access to a new
structural parameter within molecules: force. The
forces produced by motor proteins (Finer et al.,
1994; Svoboda et al., 1993), the binding forces of
receptor ligand systems (Florin et al., 1994) as well
as complementary DNA strands (Essevaz-Roulet
et al., 1997) have been measured. Recently, the
forces required to unfold proteins have been determined (Kellermayer et al., 1997; Oberhauser et al.,
1998; Rief et al., 1997a, 1998b; Tskhovrebova et al.,
1997). Until recently, information on the stability of
proteins could only be obtained by measuring the
loss of structure under denaturing conditions
(denaturing agents, temperature, pH), from which
folding free energies could be obtained. Free
Present address: J. Pascual, The Scripps Research
Institute 1050 North Torrey Pines Road, La Jolla, CA
92037, USA.
Abbreviations used: Ig, immunoglobulin; Fn3,
®bronectin III; WLC, worm-like chain; PBS, phosphatebuffered saline.
E-mail address of the corresponding author:
[email protected]
0022-2836/99/070553±09 $30.00/0
energy, however, does not provide direct information on mechanical stability. For mechanical
stability, it is important how the free energy varies
as a function of the spatial coordinates. Generally,
the multidimensional energy landscape of protein
folding is complex (Onuchic et al., 1997). However,
in a simple, one-dimensional picture a shallow
unfolding potential will lead to lower unfolding
forces than a steep one, even if the depth of the
potential well is similar. Thus, in two proteins the
same free energy of folding can lead to completely
different unfolding forces if the energy is distributed over different lengths.
Because many proteins have mechanical function
(cytoskeletal proteins, muscle proteins), measurement of their mechanical stability also provides
functional information. Using single molecule force
spectroscopy (Figure 1) we have recently succeeded to measure the forces required to unfold
single immunoglobulin (Ig) domains in the muscle
protein titin (Rief et al., 1997a, 1998). These data
showed that titin domains are so stable that they
do not unfold under conditions of normal muscle
operation. Similar forces are required to unfold
®bronectin III (Fn3) domains of the cell adhesion
protein tenascin (Oberhauser et al., 1998; Rief et al.,
1998b). Both Ig and Fn3 domains fold into compact
b-barrel structures.
Spectrin is a major component of the membraneassociated skeleton in erythrocytes. As such, it
# 1999 Academic Press
554
cross-links ®lamentous actin and contributes to the
mechanical properties of the cell (Bloch & Pumplin,
1992; Elgsaeter et al., 1986). Spectrin consists of two
subunits, b and a-chain, which form laterally
associated heterodimers (McGough & Josephs,
1990; Shotton et al., 1979). The two dimers interact
and form a head-to-head tetramer. The main part
of both chains consists of homologous repeats.
Each of these repeats (106 amino acid residues;
Speicher & Marchesi, 1984) forms a triple-helical,
antiparallel coiled-coil (Pascual et al., 1997; Yan
et al., 1993). Similar repeats occur in a variety of
proteins belonging to the spectrin superfamily
(alpha-actinin, dystrophin). Measurements of the
melting temperature result in similar values for a
spectrin repeat (53 C; DeSilva et al., 1997) and for
titin Ig domains (50-70 C; Politou et al., 1995), thus
predicting similar stabilities for these structurally
different domains. Whether this is also true for
mechanical stability is the question we address
here.
Results
Figure 2 shows a force versus extension curve of
a recombinant construct of the muscle protein titin
comprising eight Ig domains. The data are taken
from a previous study (Rief et al., 1997a). The
sequential unfolding of titin Ig domains leads to a
pronounced sawtooth pattern. We could show that
Figure 1. Schematics of a force spectroscopy experiment on a modular protein. The protein is adsorbed to
a gold or a mica surface and picked up by the AFM tip.
The domains spanning the distance between the tip and
the surface can now be mechanically unfolded. The
force is measured via the de¯ection of the AFM cantilever and is recorded as a function of the elongation.
Spectrin Unfolding Forces
the slope leading up to each peak is only determined by the elasticity of the already unfolded
polypeptide (Rief et al., 1997a). At the peak force
the weakest of the folded Ig domains in the chain
unfolds in an all-or-none event, adding an
additional stretch of unravelled polypeptide to the
chain. Hence, the absolute value of the peak force
marks the unfolding force of a domain, and the
spacing to the following peak re¯ects the gain in
length during a transition from the folded con®guration to the fully unravelled polypeptide
strand and corresponded to the 89 amino acid residues folded in an Ig domain.
In order to describe the polypeptide elasticity we
applied the WLC (worm-like chain) model
(equation (1)). However, it turns out that the WLC
model with a single parameter p cannot model the
polypeptide elasticity equally well over the complete force range (0-300 pN). This is shown in
Figure 2 where the left-hand slopes of the unfolding traces are ®t with equation (1) using
p ˆ 0.8 nm (continuous lines) and p ˆ 0.4 nm (broken lines). For forces up to 50 pN, p ˆ 0.8 nm
describes the polypeptide elasticity well. However,
above 50 pN clear deviations between these WLC
curves and the data can be seen. This is due to the
fact that additional contributions from bond angle
deformations become important at elevated forces.
A persistence length of 0.4 nm describes the polypeptide elasticity better in the range from 50 to 300
pN (broken lines; cf. Rief et al., 1997a). Here, the
unfolding forces of spectrin domains are well
below 50 pN and thus p ˆ 0.8 nm is the appropriate value. We are using the WLC model to obtain
precise information about the gain in length upon
domain unfolding. As is shown in Figure 2, the
average difference in contour length between two
adjacent unfolding peaks of the titin construct is
L ˆ 26.6 nm. It is known from the amino acid
sequence that 89 amino acid residues are folded in
each Ig domain within this construct. The titin construct can thus be used as a template for other protein unfolding curves to obtain the number of
amino acid residues folded in its units (Rief et al.,
1998b).
Figure 3(a) shows three typical force curves
taken on native spectrin. When the molecules are
elongated beyond ca. 100 nm a very characteristic
pattern of peaks appears. No difference in the
traces could be observed when mica was used as
substrate instead of gold.
The peak height of the spectrin traces lies
between 25 and 35 pN. The black lines superimposed onto the upper trace of Figure 3 are ®ts of
the contour length L to the left-hand slopes of the
peaks according to the WLC model equation (1)
using p ˆ 0.8 nm. Each peak was ®tted seperately.
The average increase in contour length from one
peak to the next is L ˆ 31.7(0.3) nm. A comparison to the 26.6 nm for Ig domains (89 amino acid
residues; see Figure 2) leads to an increase in polypeptide length of 106(1) amino acid residues per
peak. This is exactly the number of residues folded
Spectrin Unfolding Forces
555
Figure 2. Unfolding traces of a recombinant construct comprising eight immunoglobulin domains of the muscle
protein titin. The WLC model ®ts to the left-hand slopes of the unfolding pattern use two different persistence lengths
p. In a force range below 50 pN p ˆ 0.8 nm models the polypeptide elasticity best (continuous lines). At higher forces
deviations due to bond angle deformation occur, so that a persistence length of 0.4 nm seems to be more appropriate
(broken lines). Each unfolding event increases the contour length of the unfolded polypeptide strand by
L ˆ 26.6 nm (p ˆ 0.8 nm) which corresponds to 89 residues folded in each domain.
in a single spectrin repeat (Speicher Marchesi,
1984). Thus, the analysis of the spectrin unfolding
traces yields the following results: under the
in¯uence of a stretching force (pulling velocity
0.3 mm/s) spectrin repeats unfold at forces between
25 and 35 pN. The repeats unfold in a cooperative
manner and no intermediate states can be
observed.
In order to exclude the possibility that the
measured forces are in¯uenced by interactions
between the a and b-chain of the heterodimer, we
performed measurements on a recombinant construct comprising the repeats 13 to 18 from chicken
brain a-spectrin. The data are shown in Figure 3(b).
Up to four peaks can be observed showing similar
spacing and peak forces as the traces on native
spectrin.
For comparison, Figure 3(c) shows unfolding
traces of a recombinant construct of alpha-actinin
comprising four spectrin like repeats (a1-a4; Young
et al., 1998). These traces exhibit up to three peaks
of similar size and spacing as those seen in the
spectrin traces.
The way the experiment is performed also
includes the possibility that more than one molecule is being picked up in parallel, especially as
both native spectrin and alpha-actinin form dimers.
Figure 4 shows an example of multiple pickup of
spectrin molecules. The trace shows a sawtooth
pattern with much higher unfolding forces. The
multiple pickup also leads to a misspacing of adjacent unfolding peaks (see the arrows). In general,
multiple pickups occur much more often than
single molecule attachment (estimated ratio 10:1).
However, both higher unfolding forces and mis-
spacing of the peaks make it easy to decide when
more than one spectrin chain has been picked up
in parallel.
Figure 5 demonstrates that not only unfolding
but also refolding of spectrin repeats is possible.
A single spectrin chain was repeatedly stretched
and relaxed. The molecule was kept in the relaxed
state for about a second. In the subsequent stretching trace the sawtooth pattern with the same spacing and peak forces as those shown in Figure 3(a)
reappears. This shows that the spectrin repeats
refold in less than a second.
Forced unfolding of domains is not a static process, and the fact that unfolding is governed by
rates makes the unfolding forces speed dependent
(Evans & Ritchie, 1997; Rief et al., 1997a). This
speed dependence of spectrin unfolding is shown
in Figure 6. The left trace showing high forces was
recorded at a pulling speed of 0.8 mm/s, the right
trace at 0.08 mm/s. As described in Experimental,
the speed dependence can be modeled with a
simple Monte Carlo simulation. The black continuous lines superimposed onto the data show simulated traces at the respective pulling speeds. We
adapted the simulations to the measured data such
that average unfolding forces at both pulling
speeds and peak spacing match the recorded data.
This yielded the lifetime of a domain at zero force
t0 ˆ 30,000 seconds and an estimate for the width
of the linearized unfolding potential, the unfolding
length xu ˆ 1.7(0.5) nm. For the WLC elasticity
p ˆ 0.8 nm and a gain in length per unfolding
event of L ˆ 31.3 nm was chosen.
Figure 7 shows how different choices of xu and
t0 affect the speed dependence of the unfolding
556
Spectrin Unfolding Forces
Figure 3. (a) Three unfolding traces of native spectrin. The continuous lines superimposed to the ®rst curve are
Ê ). The gain in length upon each unfolding event is 31.7 nm, which corresponds to the 106 amino
WLC ®ts (p ˆ 0.8 A
acid residues folded in each spectrin repeat. (b) Unfolding traces recorded on recombinant constructs comprising six
spectrin repeats from a-spectrin. (c) Unfolding traces recorded on recombinant constructs comprising four spectrin
like repeats of a-actinin. Forces and peak spacing are similar to the traces of native spectrin.
forces in our simulations: it has been shown theoretically that the unbinding force of a receptor
ligand system is supposed to depend logarithmically on the pulling speed over a wide range of
pulling speeds (Evans & Ritchie, 1997; Izrailev et al.,
1997). In previous studies we found that this logarithmic dependence also holds for the forced
unfolding of Ig and FN3 domains (Rief et al.,
1997a, 1998b). Applying this model to the unfolding of spectrin domains it is, therefore, suf®cient to
Figure 4. Record from native spectrin showing more
than a single molecule spanning tip and surface. The
forces are higher than with single molecules (cf. Figure 3)
and the peak spacing is irregular (see the arrows).
measure the average unfolding force at only two
distinct pulling speeds, in our case 0.8 mm/s and
0.08 mm/s. As predicted (Izrailev et al., 1997), varying t0 adds an offset to the lines shown in Figure 7,
whereas xu affects their slope. Therefore, in our
simulations we ®rst varied xu to match the slope
and in a second step we varied t0 to match the
Figure 5. Repeated stretching and relaxing cycles on a
single spectrin molecule. Several domains refold in less
than a second.
Spectrin Unfolding Forces
557
Figure 6. Dependence of the unfolding force on the pulling speed. The left trace recorded at 0.8 mm/s shows higher
forces than the right trace (0.08 mm/s). The black continuous lines superimposed onto the data show the results of a
Monte Carlo simulation (see the text).
absolute values of the measured forces. The black
line in Figure 7 shows the measured speed dependence (interpolating logarithmically between the
two data points). The black line falls on top of the
simulated speed dependence using xu ˆ 1.7 nm
and t0 ˆ 30,000 s (data not shown). The grey
broken lines are the result of the Monte Carlo
simulation at parameters of xu ˆ 1 nm, t0 ˆ 400 s
and xu ˆ 2.5 nm, t0 ˆ 6 106 seconds, respectively.
Simulated unfolding events (n ˆ 100) were averaged per point. In addition to the slope of the lines
xu also affects the width of the unfolding force distribution (error bars in Figure 7; see Izrailev et al.,
1997). Figure 7 shows that an estimate for xu can
be given with a resolution of about 0.5 nm. However, for t0 only the order of magnitude can be
given.
Discussion
It has been an issue of debate whether the individual repeats in spectrin fold independently from
each other (DeSilva et al., 1997; Menhart et al.,
1996). The thermal stability of expression constructs of the ®rst domain of the a-chain depends
very sensitively on the phasing of the motifs.
A construct comprising residues 49-155 (Lusitani
et al., 1994) proved far less stable than a construct
with residues 50-158 (Kotula et al., 1993). This problem sometimes leads to contradictory conclusions
(DeSilva et al., 1997; Menhart et al., 1996). The data
in Figure 3 demonstrate that under mechanical
stress the spectrin repeats predominantly break as
well de®ned units. The high accuracy of the, peak
spacing (106(1) residues) clearly reveals these
units as spectrin repeats. If stabilizing effects of
neighboring domains prevailed, one would not
expect the spectrin structure to break in units corresponding with single repeats. In this case different spacings should occur. The observation that in
some traces (Figure 6, right trace; and Figure 3(a),
second unfolding trace) two domains seem to
break at once could re¯ect a certain stabilizing
effect of adjacent domain, possibly mediated
through a long a-helix shared between the
domains.
As mentioned above, the sawtooth pattern in the
spectrin curves with its 31.7 nm spacing means
that the mechanically forced unfolding of a single
spectrin domain is a highly cooperative process.
As soon as the maximum force is reached the
domain breaks and either completely loses structure, or the remaining structural elements after the
®rst burst are so weak that they do not in¯uence
the following slope any more. As can be seen from
the ®ts to the ®rst curve in Figure 3(a), the slopes
can be well ®tted by a mere polymer elasticity
model. Any deviation from these ®ts would have
to be attributed to remainders of secondary structure. At this point, however, one has to mention
that such effects could be burried in the noise of
our measurements; but compared with the maximum force their contributions are clearly minor.
This ®nding is in agreement with measurements of
thermal unfolding of spectrin domains where no
intermediates could be observed and unfolding
could be modeled as a two state process (DeSilva
et al., 1997). Mechanical unfolding was found to be
cooperative in titin Ig and Fn3 domains (Rief et al.,
1997a), as well as in Fn3 domains of Tenascin
(Oberhauser et al., 1998; see also Figure 1). It seems
to be a common feature of these domains, that
they completely lose mechanical stability as soon
as their core is broken up.
As demonstrated in Figure 5, it is also possible
to observe refolding in these single molecule experiments. The preliminary analysis of these experiments shows that spectrin repeats refold in less
than a second. At present the maximum pulling
speed accessible with commercially available AFM
cantilevers is at around 1 mm/s. At a higher speed
the hydrodynamic forces of the cantilever spring
being dragged through the buffer distorts the
obtained curves to such an extent that the analysis
of the spectrin unfolding curves gets dif®cult.
Thus, an analysis of the refolding kinectics down
to the millisecond range is not possible to date.
The development of smaller cantilevers with low
spring constants and less hydrodynamic drag will
allow for faster pulling cycles, and thus more
detailed experiments in the near future.
The refolding experiments also provide information on the contribution of protein-surface inter-
558
actions in our experiments. It is a reasonable concern that interactions between substrate and protein might affect the measured unfolding forces, as
well as the refolding to a considerable degree. If,
however, the protein-surface interactions dominated the interactions leading to proper domain
folding, one would not expect a regular, wellde®ned spacing in the repeated unfolding-refolding cycles exactly corresponding to the length of
single repeats as can be seen in Figure 5. This
shows that internal interactions within the domains
still prevail, which is also corroborated by the fact
that exactly the same unfolding forces are
measured on surfaces as different as mica and
gold. Gold coated AFM tips or the addition of
Tween20 or bovine serum albumin to the buffer
during the experiment does not change the forces
(data not shown).
The most prominent result of our spectrin
unfolding experiments concerns the magnitude of
the unfolding force of the domains. The difference
in unfolding forces between titin Ig domains
(Figure 2) and spectrin-like repeats of up to factor
of 10 is dramatic. On the other hand, the melting
temperatures of titin Ig domains (50-70 C; Politou
et al., 1995) and spectrin repeats (53 C; DeSiliva
et al., 1997) are rather similar. Melting temperatures
are correlated with the free energy of activation for
the unfolding process. Obviously a comparison of
free energies alone cannot explain the huge difference in mechanical stability. It is also important to
know how the free energy varies with spatial coordinates. As described in Experimental, measuring
the speed dependence of the unfolding force yields
information about the width of the unfolding
potential along the direction of pulling. The onedimensional model with its linear approximation
of the potential as expressed in equation (2) is certainly not a complete description of the multidimensional energy landscape of protein folding,
and the obtained numbers for the unfolding length
xu should be only taken as an estimate of the
thermally averaged potential with the boundary
condition of an external pulling force. However, xu
provides a new parameter that has not been experimentally accessible before. Comparing the xu
values of Ig domains (0.3 nm; Rief et al., 1997a)
and spectrin domains (1.5 nm), it becomes obvious
why the differences in forces are so dramatic. The
measured unfolding forces F of spectrin domains
are by nearly the same factor lower as the unfolding length xu is higher. The product F, xu, which
has the dimension of energy, leads to approximately the same value for both spectrin and Ig
domains.
What are the reasons for the big difference in
unfolding force between b-barrels and a-helix bundles? Both Ig and Fn3 domains form a compact
b-barrel structure in which adjacent strands are
connected by hydrogen bonds. The process of
mechanically forced unfolding of these barrels,
explaining high forces and short unfolding lengths,
has been recently elucidated by molecular
Spectrin Unfolding Forces
dynamics simulations (Lu et al., 1998). These
showed that several hydrogen bonds are loaded in
parallel until they yield and the domain completely
loses structure. In contrast to b-barrel structures,
the tertiary structure of spectrin repeats is not
stabilized by hydrogen bonds. The hydrogen
bonds in a-helices just stabilize the helix itself, but
not the whole bundle. Thus, the tertiary structure
is mostly maintained by a hydrophobic interaction
which has a longer range and leads to smaller
forces. Upon rupture of the helix bundle the
remaining alpha-helices do not show any measurable mechanical stability any more. This may be
understood considering the destabilizing effect of
the hydrophobic parts of the helices now being
exposed to the solvent. Even if the helices
remained fully intact upon further stretching, the
hydrogen bonds within the helices would be
loaded in series, thus again leading to a weak
structure. From this we anticipate that lower mechanical stability may be frequently observed in
coiled-coil structures as compared with b-sheet
domains. Attributing the unfolding forces purely
to hydrogen bonds in b-barrels and to hydrophobic
interactions in the case of a-helices is clearly an
oversimpli®cation. Nevertheless, the measured
interaction lengths and forces indicate a drastic
difference between these two types of domains.
Molecular dynamics simulations like those
described by Lu et al. (1998) will provide a more
detailed insight into forced unfolding of spectrin
domains.
It remains to be seen whether the very different
mechanical stabilities of these two different folds
also has physiological relevance. In the case of
titin, the very high stability of the protein may prevent the sarcomer from losing structure during
muscle operation. Whether the comparatively low
unfolding forces of spectrin repeats have importance for the function of spectrin as part of the
membrane skeleton has to be shown in the future.
Experimental
Expression of the spectrin construct
The expression construct, spanning from repeat 13 to
18, was generated from the cDNA for the a-subunit of
chicken brain spectrin (Wasenius et al., 1989) by standard
methods using polymerase chain reaction (PCR). The
PCR product was puri®ed and ligated to a pHAT2 vector (Peranen et al., 1996) for transformation of the Escherichia coli strain BL21 (DE3). DNA sequencing con®rmed
the identity of the insert. The clones were grown overnight at 37 C in LB medium containing 100 mg/ml
ampicilin and diluted 1:100 into one volume of
LB ‡ ampicilin. IPTG (0.5 mM) was added to induce
expression when the absorbance at 600 nm was 0.5.
After shaking for three hours at 37 C, the cells were harvested by centrifugation and resuspended in 50 mM
Tris-HCl (pH 8.0). After passage through a French press
and centrifugation to pellet unbroken cells and debris,
the supernatant was loaded onto a Ni-NTA column. The
bound protein was eluted with a Tris-HCl buffer containing 100 mM imidazole. These fractions were concen-
559
Spectrin Unfolding Forces
trated and further puri®ed by gel ®ltration on a Superdex 200 column using 20 mM potassium phosphate buffer (pH 7.0).
Sample preparation
Spectrin extracted from human erythrocytes was purchased from Sigma (Sigma, Deisenhofen, Germany). In
order to split the heterodimer, spectrin was incubated
for an hour at pH 11 (Fujita et al., 1998; 20 mM Tris buffer titrated with NaOH, 100 mg/ml protein concentration). The proteins were then allowed to adsorb onto
a freshly evaporated gold surface or a freshly cleaved
mica surface from a 50 ml drop of the same solution.
After ten minutes of incubation the sample was rinsed
with PBS (phosphate-buffered saline (pH 7.4), 150 mM
NaCl). All measurements were carried out in PBS.
Force measurements
Force measurements were carried out with a custom
built force spectrometer based on the AFM technology
(Rief et al., 1997b). Commercially available silicon nitride
cantilevers (Park Scienti®c, Stanford) were used as force
sensors (kC ˆ 7-20 mN/m). The spring constants were
determined for each cantilever by measuring the amplitude of its thermal ¯uctuations (Butt & Jaschke, 1995;
Florin et al., 1995; Hutter & Bechhoefer, 1994). Force
curves were recorded at piezo extension velocities of
0.05-0.8 mm/s.
Figure 1 depicts a force spectroscopic experiment performed on a modular protein. The protein is adsorbed to
a gold surface. The AFM tip is carefully brought into
contact with the protein-coated surface and the proteins
are picked up by the tip via adsorption. It has been
shown in various studies that adsorption can lead to
very high connecting forces (>700 pN; Li et al., 1998; Rief
et al., 1997a,b). The pickup can occur at any domain
along the protein. The mechanical stability of the
domains spanning the gap between tip and gold can
then be probed in force versus extension traces. The force
is measured via the de¯ection of the AFM cantilever and
the extension is controled by a piezo translator.
Worm-like chain (WLC) model
In order to model the force versus extension characteristics of an unfolded polypeptide chain and to obtain
quantitative information about the gain in polypeptide
length upon domain unfolding, the following interpolation formula of the WLC model (Bustamante et al.,
1994) was used:
kB T
1
1 x
F†x† ˆ
‡
…1†
ÿ
p 4…1 ÿ x=L†2 4 L
The persistence length p describes the polymer stiffness,
kB is Boltzmann's constant, L is the contour length and T
the temperature. The p value has to be chosen so that
equation (1) models the force versus extension characteristics of a polypeptide chain.
Figure 7. Average unfolding forces at the two different pulling speeds (0.08 and 0.8 mm/s). The black continuous
line shows the measured data. The grey broken lines show averaged unfolding forces obtained in Monte Carlo simulations with varying parameters (see the text). The width of force distributions (error bars) depends on the choice
of xu.
560
Spectrin Unfolding Forces
Monte Carlo simulation
To model the measured unfolding traces of spectrin, a
simple Monte Carlo simulation is performed as follows
(for details, see Rief et al., 1998a): the force due to stretching the polypeptide chain is calculated using the WLC
model (equation (1)) with a persistence length p of
0.8 nm. The probability of unfolding for each of the
domains was calculated as P ˆ t/t, where t is the
polling interval and t is the lifetime of a domain given
by (Bell, 1978; Evans & Ritchie, 1997):
t…F† ˆ t0 eÿFxu =kB T
…2†
The t0 value is the lifetime of a domain at zero force, F is
the applied force and xu is the width of the unfolding
potential. The simulation is done by (i) stretching the
polypeptide chain by a small amount; (ii) computing the
resulting force using the WLC model; (iii) calculating the
domain unfolding probability for that force and then
polling the domains with a random number generator in
order to de®ne their status. With each unfolding event,
the contour length L of the polypeptide strand increases
by L. By adjusting the parameters t0 and xu so that the
obtained average unfolding forces match the data at
different pulling speed (see Figures 6 and 7) values for t0
and xu can be obtained. Equal stability was assumed in
the simulations for all spectrin domains. Thus, the simulations re¯ect average properties of the domains.
Acknowledgments
We are indebted to Mathias Gautel and Paul Young
for generously providing the alpha-actinin construct.
We highly appreciate helpful discussions with Mathias
Gautel. This work was supported by the Deutsche
Forschungsgemeinschaft.
References
Bell, G. I. (1978). Models for the speci®c adhesion of
cells to cells. Science, 200, 618-627.
Bloch, R. J. & Pumplin, D. W. (1992). A model of spectrin as a concertina in the erythrocyte membrane
skeleton. Trends Cell Biol. 2(7), 186-189.
Bustamante, C., Marko, J. F., Siggia, E. D. & Smith, S.
(1994). Entropic elasticity of l-phage DNA. Science,
265, 1599-1600.
Butt, H.-J. & Jaschke, M. (1995). Calculation of thermal
noise in atomic force microscopy. Nanotechnology,
6(1), 1-7.
DeSilva, T. M., Harper, S. L., Kotula, L., Hensley, P.,
Curtis, P. J., Otvos, L., Jr & Speicher, D. W. (1997).
Physical properties of a single-motif erythrocyte
spectrin peptide: a highly stable independently folding unit. Biochemistry, 36(13), 3991-3997.
Elgsaeter, A., Stokke, B. T., Mikkelsen, A. & Branton, D.
(1986). The molecular basis of erythrocyte shape.
Science, 234(4781), 1217-1233.
Essevaz-Roulet, B., Bockelmann, U. & Heslot, F. (1997).
Mechanical separation of the complementary
strands of DNA. Proc. Natl Acad. Sci. USA, 94(22),
11935-11940.
Evans, E. & Ritchie, K. (1997). Dynamic strength of molecular adhesion bonds. Biophys. J. 72, 1541-1555.
Finer, J. T., Simmons, R. M. & Spudich, J. A. (1994).
Single myosin molecule mechanics: picoNewton
forces and nanometer steps. Nature, 368, 113-119.
Florin, E.-L., Moy, V. T. & Gaub, H. E. (1994). Adhesive
forces between individual ligand-receptor pairs.
Science, 264, 415-417.
Florin, E. L., Rief, M., Lehmann, H., Ludwig, M.,
Dornmair, C., Moy, V. T. & Gaub, H. E. (1995). Sensing speci®c molecular interactions with the atomic
force microscope. Biosens. Bioelectron. 10(9-10), 895901.
Fujita, T., Ralston, G. B. & Morris, M. B. (1998). Biophysical properties of human erythrocyte spectrin
at alkaline pH: implications for spectrin structure,
function, and association. Biochemistry, 37(1), 264271.
Hutter, J. L. & Bechhoefer, J. (1994). Calibration of
atomic-force microscope tips. Rev. Sci. Instrum.
64(7), 1868-1873.
Izrailev, S., Stepaniants, S., Balsera, M., Oono, Y. &
Schulten, K. (1997). Molecular dynamics study of
unbinding of the avidin-biotin complex. Biophys. J.
72, 1568-1581.
Kellermayer, M. S., Smith, S. B., Granzier, H. L. &
Bustamante, C. (1997). Folding-unfolding transitions
in single titin molecules characterized with laser
tweezers. Science, 276, 1112-1116.
Kishino, A. & Yanagida, T. (1988). Force measurements
by micromanipulation of a single actin ®lament by
glass needles. Nature, 334, 74-76.
Kotula, L., DeSilva, T. M., Speicher, D. W. & Curtis, P. J.
(1993). Functional characterization of recombinant
human red cell alpha-spectrin polypeptides containing the tetramer binding site. J. Biol. Chem. 268(20),
14788-14793.
Li, H., Rief, M., Oesterhelt, F. & Gaub, H. E. (1998).
Single molecule force spectroscopy on xanthan by
AFM. Advan. Materials, 10, 316-319.
Lu, H., Isralewitz, B., Krammer, A., Vogel, V. &
Schulten, K. (1998). Unfolding of titin immunoglobulin domains by steered molecular dynamics
simulation. Biophys. J. 75(2), 662-671.
Lusitani, D. M., Qtaishat, N., LaBrake, C. C., Yu, R. N.,
Davis, J., Kelley, M. R. & Fung, L. W. (1994). The
®rst human alpha-spectrin structural domain begins
with serine. J. Biol. Chem. 269(42), 25955-25958.
McGough, A. M. & Josephs, R. (1990). On the structure
of erythrocyte spectrin in partially expanded membrane skeletons. Proc. Natl Acad. Sci. USA, 87(13),
5208-5212.
Menhart, N., Mitchell, T., Lusitani, D., Topouzian, N. &
Fung, L. W. (1996). Peptides with more than one
106-amino acid sequence motif are needed to mimic
the structural stability of spectrin. J. Biol. Chem.
271(48), 30410-30416.
Oberhauser, A. F., Marszalek, P. E., Erickson, H. P. &
Fernandez, J. M. (1998). The molecular elasticity of
the extracellular matrix protein tenascin. Nature,
393, 181-185.
Onuchic, J. N., Luthey-Schulten, Z. & Wolynes, P. G.
(1997). Theory of protein folding: the energy landscape perspective. Annu. Rev. Phys. Chem. 48, 545600.
Pascual, J., Pfuhl, M., Walther, D., Saraste, M. & Nilges,
M. (1997). Solution structure of the spectrin repeat:
a left-handed antiparallel triple-helical coiled-coil.
J. Mol. Biol. 273(3), 740-751.
Peranen, J., Rikkonen, M., Hyvonen, M. & Kaariainen,
L. (1996). T7 vectors with modi®ed T7lac promoter
Spectrin Unfolding Forces
for expression of proteins in Escherichia coli. Anal.
Biochem. 236(2), 371-373.
Politou, A. S., Thomas, D. J. & Pastore, A. (1995). The
folding and stability of titin immunoglobulin-like
modules, with implications for the mechanism of
elasticity. Biophys. J. 69, 2601-2610.
Rief, M. M., Gautel, F., Oesterhelt, F., Fernandez, J. M.
& Gaub, H. E. (1997a). Reversible unfolding of individual titin immunoglobulin domains by AFM.
Science, 276, 1109-1112.
Rief, M., Oesterhelt, F., Heymann, B. & Gaub, H. E.
(1997b). Single molecule force spectroscopy on polysaccharides by AFM. Science, 275, 1295-1297.
Rief, M., Fernandex, J. M. & Gaub, H. E. (1998a).
Elastically coupled two-level-systems as a model for
biopolymer extensibility. Phys. Rev. Letters, 81, 47644767.
Rief, M., Gautel, M., Schemmel, A. & Gaub, H. E.
(1998b). The mechanical stability of immunoglobulin and ®bronection III domains in the muscle
protein titin measured by AFM. Biophys. J. 75(6),
3008-3014.
Shotton, D. M., Burke, B. E. & Branton, D. (1979). The
molecular structure of human erythrocyte spectrin.
Biophysical and electron microscopic studies. J. Mol.
Biol. 131(2), 303-329.
561
Smith, S. B., Finzi, L. & Bustamante, C. (1992). Direct
mechanical measurements of the elasticity of single
DNA molecules by using magnetic beads. Science,
258(13), 1122-1126.
Speicher, D. W. & Marchesi, V. T. (1984). Erythrocyte
spectrin is comprised of many homologous triple
helical segments. Nature, 311(5982), 177-180.
Svoboda, K., Schmidt, C. F., Schnapp, B. J. & Block,
S. M. (1993). Direct observation of kinesin stepping
by optical trapping interferometry. Nature, 365, 721727.
Tskhovrebova, L., Trinick, J., Sleep, J. A. & Simmons,
R. M. (1997). Elasticity and unfolding of single
molecules of the giant muscle protein titin. Nature,
387, 308-312.
Wasenius, V. M., Saraste, M., Salven, P., Eramaa, M.,
Holm, L. & Lehto, V. P. (1989). Primary structure of
the brain alpha-spectrin. J. Cell. Biol. 108(1), 79-93.
Yan, Y., Winograd, E., Viel, A., Cronin, T., Harrison,
S. C. & Branton, D. (1993). Crystal structure of the
repetitive segments of spectrin. Science, 262(5142),
2027-2030.
Young, R., Ferguson, C., Banuelos, S. & Gautel, M.
(1998). Molecular structure of the sarcomeric Z-disk:
two types of titin interactions lead to an asymmetrical sorting of alpha-actinin. EMBO J. 17(6), 16141624.
Edited by W. Baumeister
(Received 18 September 1998; received in revised form 30 November 1998; accepted 30 November 1998)