doi:10.1016/S0022-2836(03)00618-1
J. Mol. Biol. (2003) 330, 867–877
Mechanical Unfolding of a Titin Ig Domain: Structure
of Transition State Revealed by Combining Atomic
Force Microscopy, Protein Engineering and Molecular
Dynamics Simulations
Robert B. Best1†, Susan B. Fowler1†, José L. Toca Herrera1
Annette Steward1, Emanuele Paci2 and Jane Clarke1*
1
Department of Chemistry
University of Cambridge, MRC
Centre for Protein Engineering
Lensfield Road, Cambridge CB2
1EW, UK
2
Department of Biochemistry
University of Zurich
Winterthurerstrasse 190, 8057
Zurich, Switzerland
Titin I27 shows a high resistance to unfolding when subject to external
force. To investigate the molecular basis of this mechanical stability,
protein engineering F-value analysis has been combined with atomic
force microscopy to investigate the structure of the barrier to forced
unfolding. The results indicate that the transition state for forced unfolding is significantly structured, since highly destabilising mutations in the
core do not affect the force required to unfold the protein. As has been
shown before, mechanical strength lies in the region of the A0 and
G-strands but, contrary to previous suggestions, the results indicate
clearly that side-chain interactions play a significant role in maintaining
mechanical stability. Since F-values calculated from molecular dynamics
simulations are the same as those determined experimentally, we can,
with confidence, use the molecular dynamics simulations to analyse the
structure of the transition state in detail, and are able to show loss of interactions between the A0 and G-strands with associated A – B and E – F loops
in the transition state. The key event is not a simple case of loss of hydrogen bonding interactions between the A0 and G-strands alone. Comparison with F-values from traditional folding studies shows differences
between the force and “no-force” transition states but, nevertheless, the
region important for kinetic stability is the same in both cases. This
explains the correspondence between hierarchy of kinetic stability
(measured in stopped-flow denaturant studies) and mechanical strength
in these titin domains.
q 2003 Elsevier Ltd. All rights reserved
*Corresponding author
Keywords: protein folding; AFM; titin; immunoglobulin; muscle
Introduction
Some proteins experience significant mechanical
stress in vivo. Experimental studies of the effect of
force on various proteins show that there is a sig† R.B.B. and S.B.F. contributed equally to this work.
Present address: J. L. Toca Herrera, Centre for
Ultrastructure Research, Universität für Bodenkultur
Wien, Gregor Mendel Str. 33, A-1180 Vienna, Austria.
Abbreviations used: AFM, atomic force microscopy;
MD, molecular dynamics; Ig, immunoglobulin; TI I27,
the 27th Ig-like domain from the I band of human
cardiac titin; ‡f and ‡o, the transition states investigated
by force and denaturant unfolding, respectively.
E-mail address of the corresponding author:
[email protected]
nificant range of mechanical strength.1 – 8 All-b
domains from proteins of muscle or the extracellular matrix resist significantly higher forces
than all-a, or mixed a/b proteins even where they
may be expected to experience stress in vivo (such
as the cytoskeletal protein spectrin). However,
there is not a simple relationship between structure
and strength. Even small changes in sequence can
alter the dynamic force spectrum of a protein.9,10
Dissecting the forced unfolding pathways of proteins in detail should advance our understanding
of the molecular basis for mechanical strength in
proteins. In experimental studies of protein
(un)folding the emphasis is on high-resolution
characterisation of all the species on the folding
pathway. States that are stable, the native and
denatured states and kinetic intermediates, as well
0022-2836/$ - see front matter q 2003 Elsevier Ltd. All rights reserved
868
Figure 1. TI I27 showing the position of the mutations
made in this study.
as the rate-determining transition state, are
accessible to experimental techniques. Molecular
dynamics (MD) simulations should be able, in
principle, to shed light on the transitions between
them. However, since simulations are generally
performed at far-from experimental conditions,
the benchmarking of simulation by experiment is
essential. An attractive feature of forced unfolding
experiments is that direct comparison between
simulation and experiment is facilitated by there
being a well-defined reaction co-ordinate, the distance between the N and C termini of the protein.
The protein that has been investigated most
extensively using atomic force microscopy (AFM)
is the 27th immunoglobulin (Ig) domain of the I
band of titin (TI I27) (Figure 1).9,11 – 20 It was
suggested initially that on application of force this
protein unfolds by the same pathway as that followed on addition of denaturant.11 The evidence
was twofold: the unfolding rate constant, extrapolated to zero force, was the same as that determined by extrapolation to 0 M denaturant; and in
both cases the transition state lay very close to the
native state; forced unfolding is associated with a
short unfolding distance, , 3 Å, and in denaturant-induced unfolding the bT† is high, . 0.9.
† bT is defined as the ratio RTmkf/meq, where mkf and
meq are the dependence of folding rate and stability on
denaturant concentration. It is a measure of the
transition state position on a scale from 0 (close to
denatured state) to 1 (close to the native state).40
Mechanical Unfolding of Titin
However, later analysis revealed that at moderate
forces ($ 100 pN), below those required to unfold
the protein completely (, 200 pN), TI I27 unfolds
to form a meta-stable intermediate that is not
observed in the denaturant-induced unfolding.12
This intermediate is observed in simulations of
forced unfolding that show that the A-strand is
detached from the body of the protein in the
intermediate.16 Mutational studies confirmed that
this intermediate is the “ground state” for forced
unfolding (Figure 2), so that the previous comparison between the denaturant-induced and forced
unfolding pathways is invalid.17,18 We have previously described a model intermediate in which
the A-strand is deleted and shown, using a combination of NMR and MD simulation that this
model is folded and stable, and has essentially the
same structure as that of the wild-type protein.17
Here, we analyse the forced unfolding pathway
further. We have previously demonstrated that
protein engineering F-value analysis can be
applied directly to the analysis of protein unfolding pathways in response to an external force.21
We show, by a combination of protein engineering,
AFM and MD simulation, that the transition state
for forced unfolding is more native-like than the
transition state observed when unfolding is
initiated by addition of denaturants. We suggest,
however, that the correlation between unfolding
rates of different titin Ig domains and their resistance to force is not coincidental: it is the same
region of the protein that is responsible for kinetic
stability in both cases.
Results
All mutations destabilise TI I27 significantly
Mutations were chosen to probe different
regions of TI I27 (Figure 1). Each of these mutants
has been characterised in the isolated TI I27
domain, both in terms of the effect on stability
and the effect on the folding kinetics.22 All have
been shown to destabilise the native state significantly (by 2.2 – 4.8 kcal mol21 (1 cal ¼ 4.184 J)).
Since the AFM experiments measure the force
required to unfold the intermediate, I, the effect of
the mutations on the stability of a model intermediate (DDGD-I), with the A-strand deleted (TI
I27-A)17 was determined (Table 1). For each
mutant, DDGD-I is similar to DDGD-N, reflecting the
extremely native-like structure of I.17 The stability
(DGD-N) of TI I27 in the polyprotein has been
shown to be the same as the stability of the isolated
domain.17
Most mutations do not significantly change the
force required to unfold the protein
The force required to unfold each mutant polyprotein was measured at a minimum of four
pulling speeds, and at least two separate data sets
869
Mechanical Unfolding of Titin
Figure 2. The forced unfolding pathway. Above
,100 pN a stable unfolding intermediate is populated,
the unfolding force is the force required to unfold this
intermediate, and k0u is the unfolding rate constant of
this intermediate, extrapolated to zero force. The unfolding distance xu reflects the distance from I to ‡.
were collected at each pulling speed. Traces were
collected according to standard criteria23 (see
Materials and Methods) and all peaks except for
the first and the last (protein detachment) were
used to determine unfolding forces. There was no
difference in the average number of peaks in a
trace for wild-type and mutants. The mean of each
data set was determined and the mean of these
means at each pulling speed is shown in Figure 3.
Also shown on each graph in Figure 3 is the force
that would be expected if all the loss in stability
upon mutation were reflected in the unfolding
reaction; i.e. if the transition state energy were not
affected by mutation at all. It is clear that most
mutations have very little effect on the experimentally measured unfolding forces. Most mutants
have little effect on the dependence of the unfolding force on the pulling speed (most mutant data
have the same gradient as the wild-type data in
Figure 3). V13A has significantly lower unfolding
forces than wild-type, but essentially the same
gradient. V86A shows both a decrease in the
unfolding forces, and a significant decrease in the
gradient.
The data were analysed using a Monte Carlo
approach, as described in Materials and Methods,
to estimate an unfolding rate at zero force ðk0u Þ and
an unfolding distance (xu) that is related to the
distance along the unfolding trajectory between
the ground state (the unfolding intermediate in
the case of TI I27) and the transition state for
unfolding (Figure 2 and Table 1).
F-Value analysis
A transition state F-value gives information
about the structure of the transition state, and is
determined by comparing the effect of mutation
on the native state directly with the effect of the
mutation on the transition state for unfolding, and
can be determined from a comparison of unfolding
rates between wild-type and mutant:
F¼12
DDG‡-N
DDGD-N
ð1Þ
where DDGD-N is the change in free energy of the
protein on mutation, and:
DDG‡-N ¼ 2RT ln
kwt
u
kmut
u
ð2Þ
mut
are the unfolding rate constants
where kwt
u and ku
of wild-type and mutant proteins, respectively.
Table 1. Effect of mutation on the stability and unfolding of TI I27
Mutant
Position
in protein
DDGD-Ia
(kcal mol21)
WT
V13A
I23A
L41A
L58A
L60A
F73L
V86A
A0 -strand
B-strand
C0 -strandf
E-strand
E-strand
F-strand
G-strand
2.37 ^ 0.08
2.89 ^ 0.09
2.67 ^ 0.08
3.61 ^ 0.11
5.27 ^ 0.17
3.06 ^ 0.12
4.78 ^ 0.18
a
xu (Å)
k0u b
(mean xu)
(s21)
Experimental
mechanical
F-valuec
Simulation
mechanical
F-valued
Experimental
denaturant
F-valuee
3.3
3.5
3.0
3.4
3.3
3.1
2.9
5.5
1.5 £ 1024
6.5 £ 1024
5.3 £ 1025
2.1 £ 1024
8.3 £ 1025
1.7 £ 1024
8.0 £ 1025
6.6 £ 1026g
0.6 ^ 0.1
1.2 ^ 0.1
0.9 ^ 0.1
1.1 ^ 0.1
1.0 ^ 0.1
1.1 ^ 0.1
0.7 ^ 0.1
0.9 ^ 0.1
0.8 ^ 0.2
0.9 ^ 0.1
0.9 ^ 0.1
0.7 ^ 0.1
0.4 ^ 0.1
20.04 ^ 0.01
0.82 ^ 0.03
0.40 ^ 0.02
0.79 ^ 0.04
0.67 ^ 0.03
0.72 ^ 0.02
0.01 ^ 0.01
g
Taken from Fowler et al.17 and refers to mutations made with the TI I27-A mutant as a model for the intermediate.
Values of k0u calculated using Monte Carlo simulations using mean xu, (3.2 Å).
c
F-values calculated by direct comparison of unfolding force, F, at a pulling speed of 500 nm s21; equation (4).
d
Fraction of native contacts at the transition state in the simulations.
e
Denaturant F-values taken from Fowler et al.22
f
The C-D loop is formally termed the C0 -strand in the accepted assignment of the structure of this type of domain.
g
Since V86A has a significantly different xu, it has been shown to unfold by a mechanism different from that used by the wildtype,10 so k0u at mean xu and an experimental F-value cannot be determined. The k0u quoted is taken from the direct Monte Carlo simulation of the data, but this cannot be compared to the k0u for all other mutants, since it does not reflect the same unfolding transition.10
An experimental F-value for this mutant has been estimated to be <0.6.10
b
870
Measuring DDGD-I
In the formalism above, the ground state for
unfolding is assumed to be the native state N. This
is not the case in TI I27. Upon application of force,
TI I27 unfolds via a structured, meta-stable intermediate: N ! I ! ‡ ! D (Figure 2). Importantly,
this intermediate is the ground state for the AFM
measurements, thus the forces measured are the
forces required to unfold I, not to unfold N.17 To
carry out a F-value analysis, therefore, it is
important to know the effect of mutation on this
ground state. For such a system:
DDG‡-I
ð3Þ
F¼12
DDGD-I
We have characterised a mutant of TI I27 with the
A-strand deleted (TI I27-A) and shown it to be a
good model for I.17 Thus, DDGD-I was evaluated by
measuring the effect of the mutations on TI I27-A,
using equilibrium denaturation (Table 1). Note
that the mutations have a very similar effect on
the stability of I and N†. It would probably not be
possible to use multimers of TI I27-A directly for
AFM experiments because the lack of a linker segment would cause the domains to contact each
other. While a generic “unstructured” linker could
be added, there is always the possibility of forming
the same backbone hydrogen bonding interactions
as the native A-strand.
Measuring DDG‡-I
In principle, the force data can be used to determine the unfolding rate along this pathway at
zero force, k0u ; directly and this can be used in
determination of DDG‡-I using equation (2). However, there is significant error associated with the
direct determination of k0u from the dynamic force
spectrum, since values of k0u are strongly coupled
to the unfolding distance between the intermediate
and transition state (xu): small errors in xu can
cause large changes in fitted unfolding rates.21 It
has been shown that more accurate F-values can
be determined for mechanical unfolding data
where wild-type and mutants have the same xu
† It should be noted that throughout we assume that TI
I27-A is a good model for I. If this assumption were not
correct then the F-values determined would have an
associated error. It is possible that the effect of a
mutation on the ground state under force will be
different from that measured in solution, but it is not
possible to measure this. Although the denatured state is
different in the equilibrium and pulling experiments, it is
reasonable to suppose that the effect of a conservative
mutation as described here will be the same on the two
denatured states. It has been shown that this holds true
for the mutant V13A (see10). The same was not true of the
mutant V86A, which is discussed in detail elsewhere.10
However, since for the other mutants there is no
difference between DG‡-I for WT and mutants
(DDG‡-I < 0) the absolute value of DDGD-I is actually
unimportant, since DDG‡-I/DDGD-I is also <0.
Mechanical Unfolding of Titin
within error, by evaluating DDG‡-I by one of three
methods, each of which essentially uses or assumes
a fixed mean xu, and the F-values determined by
all three methods are the same, within error.21 The
assumption of a fixed mean xu is akin to assuming
the same transition state, which is in any case a
fundamental requirement of F-value analysis.
(i) xu is fixed to a mean value and the Monte
Carlo simulations are performed with this
parameter fixed. (Mean xu determined for wildtype and all mutants except V86A ¼ 3.2 Å).
(ii) The unfolding forces for wild-type and
mutant proteins can be compared directly at a
given pulling speed (equation (4); Materials and
Methods).
(iii) The pulling speeds are compared for wildtype and mutant proteins at a given force.
The experimental F-values, determined using
method (ii) are reported in Table 1. Note that
F-value analysis is valid only where the mutation
does not change the mechanism for unfolding.
This can be assumed to be true for most of the
mutants described here, where the mutation does
not change the dependence of force on pulling
speed (i.e. they have the same xu, as wild-type
within error). For the mutant V86A, however,
there is evidence that the mutation changes the
unfolding mechanism, since the pulling speed
dependence is significantly different from that of
the wild-type, a F-value cannot be determined
using this analysis. This mutant has been discussed
in detail elsewhere.10
Determining “limiting forces” where F 5 1,
or F 5 0
The limiting conditions describing F ¼ 1 and
F ¼ 0 can be determined as follows for each
mutant and are shown for each mutant in Figure 3.
Upper limit, F ¼1
Where the mutation is in a region of the protein
that is as fully formed in ‡ as in I, then the barrier
to unfolding, DG‡-I, will remain the same height
and the force required to unfold the mutant will
be the same as wild-type. Thus the wild-type data
define the limiting case for forces expected for
F ¼ 1. Where mutant unfolding forces fall close to
the wild-type forces we can say that F < 1.
Lower limit, F ¼0
Where the mutation is in a region that is completely unfolded in ‡, the change in the height
of the free energy barrier is equal to the full
loss in free energy of I upon mutation (i.e.
DDG‡-I ¼ DDGD-I). This F ¼ 0 limit will depend on
how destabilising the mutation is, and can be
determined from the wild-type data and equation
Mechanical Unfolding of Titin
871
Figure 3. Most mutations do not affect either the mean unfolding force or the pulling speed dependence of the
unfolding force. (Wild-type data, filled circles and continuous line; mutant data, open circles and broken line). The fit
of the data using a mean value of xu (3.2 Å) is shown, except for V86A, where the dependence of unfolding force on
the pulling speed is significantly different. The dotted line represents the force expected if the F-value were 0, where
DDG‡-I ¼ DDGD-I.
(4) (Materials and Methods). Where mutant
unfolding forces fall close to this limit we can say
that F < 0.
To have confidence in the ability of the experimental data to distinguish these cases, the mutants
were chosen such that DDGD-I was . 2 kcal mol21.
Where the unfolding forces fall between these two
limits, the mutant has a partial F-value.
Identification of the transition state for
unfolding in MD simulations
MD simulations of forced unfolding were performed at three different forces (300, 350 and
400 pN) as described (see Materials and Methods).
In all simulations, a meta-stable intermediate is
evident, at an N – C distance (rNC) of approximately
53 Å. At forces of 300 pN or lower, this intermediate does not unfold further, within the 3 ns
timescale of the simulations. This state corresponds
to the TI I27-A model intermediate characterised
extensively by simulation and experiment.17
At higher forces, the protein unfolds further (see,
for example Figure 5 of Fowler et al.17). In some
simulations complete unfolding is preceded by a
slow unfolding phase detected at rNC , 57.5 Å
corresponding to a rearrangement of the A0 and
G-strands with formation of non-native hydrogen
bonds between them, before the structure is disrupted completely. The transition state for forced
unfolding (‡f) is assumed to be the last configuration before the protein starts stretching at high
872
speed under force. Being an unstable state, it is not
possible to sample it extensively. However, since
we performed multiple simulations, we were able
to collect a considerable number (263) of these
unstable configurations for analysis, all characterised by an rNC between 56 Å and 58 Å. Average
properties of these conformations show that the
protein remains quite native-like at the transition
state for forced unfolding; the RMSD from native
state is between 3 Å and 5 Å (3.9 Å on average),
while the radius of gyration (Rg) increases by 5%
and the solvent-accessible surface increases by 8%.
Evaluating F-values in MD simulations
It has been shown that a F-value can be determined from MD simulations of unfolding by
measuring the fraction of native contacts remaining in a transition state structure.24 FMD is calculated as the fraction of native contacts in the
transition state structures, compared to the fraction
present in the unfolding intermediate. FMD values
calculated for the same residues as those measured
experimentally are reported in Table 1.
Discussion
Choice of mutants
In any F-value analysis, the choice of mutation is
critical.25 The mutation should not be likely to
cause any significant perturbation of the native
state structure, nor should it be expected to have a
significant effect on the stability of the denatured
state. To this end, the mutation should be a conservative deletion, removing specific interactions,
not adding new ones and not changing the chemical (polar/non-polar) nature of the side-chain. The
mutations described here all meet these criteria
and were chosen to probe all regions of TI I27 without bias to regions of low or high F-values in
denaturant. The effect of the mutation on the
stability of the domain in the eight module protein
used for AFM experiments is the same as in the
single module.17 All mutants were chosen to have
a significant change in DGD-I, so that any change in
force upon mutation is likely to be outside the
error of the wild-type data.
Most mutations do not change xu and
k0u significantly
It is apparent that most of the mutants do not
change the dependence of the force on the pulling
speed significantly (the slope of Figure 3), with the
exception of V86A, which changes this slope (and
thus xu) significantly (Figure 3). Thus to determine
accurate F-values DDG‡-I was determined by direct
comparison of wild-type and mutant data, for all
mutants except V86A, as outlined in Materials and
Methods.21 Most mutants have the same k0u , within
error, as wild-type (i.e. F < 1). This is qualitatively
Mechanical Unfolding of Titin
apparent from direct comparison of the data with
wild-type (Figure 3). None of the mutants has F
equal or close to zero. Only V13A has a significantly reduced F-value (F < 0.6). Interestingly,
although I23A has F close to 1 (within error), the
mean force required to unfold this mutant is higher
at all pulling speeds than that required for the
wild-type. This mutant may really have F . 1. If
true, this would suggest that this mutation
destabilises the transition state more than the intermediate and might indicate that the structure
around residue 23 is more compact in ‡f than in I;
that is, residue 23 may be stabilized in ‡f relative
to I due to the formation of additional (possibly
non-native) packing interactions.
It is not possible to calculate a F-value directly
for V86A in the G-strand, since there is evidence
that the mechanism for unfolding is changing in
this mutant. It has been shown that this mutant is,
in fact, unfolding directly from the native state;
thus, the unfolding distance (xu) is significantly
longer than for the wild-type and the other
mutants.10 However, the change in unfolding
mechanism indicates that mutation of this sidechain changes the unfolding activation energy, i.e.
it is likely that this mutation has more effect on
the ground state for unfolding than on the
transition state. This side-chain is apparently less
structured in ‡f than in I (i.e. F , 1). It has been
estimated that the F-value for this V86A mutant is
< 0.6.10
Structure of the transition state
The picture from the experimental F-values is
clear: the transition state for forced unfolding (‡f)
is very native-like, except in the A-strand and
the region encompassing the A0 -strand and the
C-terminal section of the G-strand. While the
number of mutants is naturally limited by the technique, experience from solution F-value analysis
shows that F-values always follow a smooth
pattern. Thus, it would be extremely unlikely for
the residues “in between” those probed to have
very different F-values. This is especially true
when all the measured F-values are close to unity,
as this would be difficult to reconcile with any
residues in between (which must contact some of
the residues which were probed) having low
F-values.
Residues 41, 58 and 60 probe the “upper”,
C-terminal part of the core (Figure 1) and contact
residues in the B, C, D, E and F-strands and the
C – D loop region. The F-values of 1 indicate that
mutations in this region affect the stability of ‡f to
the same extent as the intermediate (and,
incidentally, the native state). The structure of this
region is not perturbed by force, before the
transition state barrier is overcome.
Residues 23 and 73 probe the “lower”,
N-terminal part of the core (Figure 1) and contact
residues in the B, C, E and F-strands, the F-G
loop and, interestingly, the early part of the
873
Mechanical Unfolding of Titin
G-strand. The high F-values indicate that this
region of the core remains completely structured
in the transition state. They also indicate that the
N-terminal portion of the G-strand remains
attached to the protein. V4A, in the A-strand,
which is in contact with residues 23 and 73, is
already detached in the unfolding intermediate,
so the F-values do not reflect loss of these
contacts.
Residues 13 and 86 in the A0 and C-terminal
region of the G-strand, are in contact close to the
C terminus of the protein. They are in contact also
with residues in the A –B and E – F loops. The intermediate F-value of V13A indicates that this region
is partially, but not completely, unstructured in ‡f.
There are insufficient data from these experimental
results to indicate what the partial F-value of
V13A represents, a weakening of all contacts, or a
complete disruption of some part of the structure,
with some contacts remaining intact. Since these
are single-molecule experiments, it is possible to
say definitively that the partial F-value does not
result from parallel pathways; since the distribution of forces in the unfolding experiments is
the same as for other mutants and wild-type, there
is no indication of a bimodal distribution of forces
that would be expected from parallel pathways
(data not shown).
Thus, in the transition state for unfolding, the
A-strand is entirely detached from the rest of the
protein, while the A0 and G-strand have lost some
of their interactions, but are not detached completely. In particular, the G-strand is apparently
completely structured towards the N-terminal part
of the strand. The experimental F-values can be
compared directly with the F-values computed
from the MD simulation. In all cases, the experimental and simulated F-values are the same,
within error (Table 1). Thus, the simulations can
be used with confidence to compare the structure
of the transition state with the native state in more
detail.
Transition state structures from a number of
simulations were analysed. All these structures
showed similar features. The RMSD from the
wild-type protein (residues in the B-F strands
only) varies between 1.7 Å and 3.7 Å, with most
variation in the relatively mobile C – D loop. The
contacts between strands B and E, E and D, and C
and F are maintained, as are all hydrogen bonds
between these strands. The core structure is
unaffected. In all structures, the A-strand is
detached completely from the protein, as is the
case in the unfolding intermediate. The main structural difference between the intermediate (I) and
native (N) structures and the transition state is the
position of the G-strand. In N and I, there are
hydrogen bonds between G and A0 , and G packs
between the A – B and E – F loops. In the transition
state structures, the G-strand is pulled “up”, away
from the A0 -strand (Figure 4). All hydrogen bonds
between G and A0 are lost, although some sidechain contacts between A0 and G remain. The con-
tacts between the G-strand and the A –B and E– F
loops are weakened significantly. However, the
G-strand retains both hydrogen bonding and sidechain contacts with the F-strand. The A0 -strand
retains cross-sheet contacts with residues in the
B-strand but loses some with both the A – B and
E –F loops, which change structure following loss
of the packing interactions with the G-strand.
Interestingly, a mutant of TI I27 that has a Cys to
Ser mutation at position 63, in the E –F loop, that
contacts both V13 and V86 has been shown to
require a lower unfolding force than wild-type TI
I27, with a significantly lower k0u (2 £ 1023 s21) but
similar xu (2.9 Å).18 Although a quantitative comparison of these data is not possible, as they refer
to a five-domain construct in which there are two
kinds of domains, with two or three other
mutations compared to the wild-type described
here, the results are consistent with the partial
breaking of contacts between the E-F loop and the
A0 and G-strands.
Our results are entirely consistent with the
previous suggestions that the A0 – G region acts as
a “mechanical clamp”.12 – 14,18 However, in contrast
to earlier suggestions, the mechanical strength
does not rest solely in the hydrogen bonding network between the A0 and G-strands.14 Side-chain
interactions between the strands and between the
A0 and G-strands and other regions of the protein,
in particular with the A – B and E– F loops also
play a critical role in determining mechanical
strength.26
Comparison with the transition state from
denaturant-induced unfolding
An extensive F-value analysis of TI I27 has been
reported, in the absence of applied force, using
denaturant-induced unfolding/refolding.22 This
protein has one of the most structured transition
states yet described (called ‡0) (Figure 5). In
essence, ‡0 is an expanded form of the native state,
with no region fully structured; no mutant has a
F-value of 1 but a number of residues have high
F-values (0.7 – 0.8) with the nucleus centred around
residues 23, 34, 58 and 73 from the B, C, E and
F-strands. Mutants in the A-strand (such as V4A)
and the loops (such as L41A) have intermediate
F-values, inferring that they are less well structured than the core, but still ordered to some
extent. Only the A0 and G-strands and associated
A-B and E-F loops are completely unstructured,
and have F ¼ 0.
The transition state for forced unfolding (‡f) is
more structured than ‡0. All the core residues
reported for ‡f in this study have significantly
lower F-values in ‡0 (Table 1). Most of the protein
is unchanged in structure by the applied force,
which acts to detach the A-strand completely, and
then to disrupt the structure in the region of the
A0 and G-strands, breaking contacts between these
strands, and between these strands and the associated loops. However, this region still maintains
874
Mechanical Unfolding of Titin
Figure 4. Structures along the forced unfolding pathway. (a) These structures are snapshots from a typical MD
unfolding trajectory. (b) Overlay of five representative transition state structures (in blue) with the structure of the
“model” intermediate TI I27-A (in red).17
some structure in ‡f, unlike ‡0, where the F-values
are close to zero (Table 1). The only region that is
more structured in ‡0 is the A-strand, which has
partial F-values (< 0.4).
It is now clear that the unfolding pathways are
not the same;17,18 TI I27 unfolds via an intermediate
that is not populated on the denaturant-induced
unfolding pathway, and the transition states have
different structures. It is easy to understand why
this should be so, force acts on specific regions of
the protein, namely the N and C termini, whereas
denaturant has a more global effect. However,
there is evidence that there are common determinants of the unfolding kinetics in the different
pathways.11 In an investigation of the forced
unfolding of two titin domains, I27 and its neighbour I28, it was observed that I28, which is much
less stable than I27, unfolded at significantly higher
forces than I27, and that this correlated with the
significantly lower unfolding rate (at 0 M denaturant) of I28.27 Furthermore, the hierarchical unfolding of a number of titin domains corresponds well
to the unfolding hierarchy observed in denaturant-unfolding studies.28,29 Why are some modules
such as TI I28 kinetically more stable than TI I27
when we compare unfolding both by denaturant
and by force?
Comparisons of the unfolding pathways of
Figure 5. The same region of the protein determines the kinetic stability along both the forced and denaturantinduced unfolding pathways. (a) A summary of results on ‡f, described here. (b) A summary of F-value data taken
from Fowler & Clarke for ‡0.22 The F-values are coloured from low (,0) in red to high (,0.7) in blue, with nucleus
residues shown in dark blue.
875
Mechanical Unfolding of Titin
Ig-like proteins have strongly suggested that they
all fold (and unfold) by similar mechanisms.22,30 – 32
Thus, it is reasonable to suppose that the same is
true of the closely related TI I27 and I28. Compare
the results from the protein engineering analysis
of TI I27 by the two methods (Figure 5). The
thermodynamic stability depends largely on the
protein core, yet mutations in the core have little
effect on the unfolding rates or unfolding forces,
since it is the least perturbed region in either ‡0 or
‡f. The A-strand has relatively little importance in
determining the kinetic stability. This is either
because it is detached completely in the unfolding
intermediate (in forced unfolding) or remains
attached (in ‡0). The only region that is crucial in
determining the kinetic stability of the protein,
whichever unfolding regime is under inspection,
is the A0 – G region towards the C terminus of the
protein. Thus, the relative stability of this region,
which will depend on the specific interactions of
side-chains, will largely determine the kinetic
stability of a titin domain, whether unfolded by
force or by chemical denaturant. This explains
why both AFM and denaturant studies observe
the same unfolding hierarchy in TI I27 and TI I28,
and suggests that denaturant-based studies will be
useful in understanding the assembly of titin
domains. Despite the common determinants of
unfolding kinetics, the similarity between the
chemical and denaturant-induced unfolding rates
must now be interpreted as a coincidence: the
proteins are unfolding from a different ground
state via a differently structured transition state, to
a very different denatured state; only the height of
the free energy barrier is similar.
proceeds rapidly and the structure no longer
resists applied force.
The unfolding pathway following addition of
force is demonstrably different from that followed
upon addition of denaturant. However, the same
region of the protein is largely responsible for
determining the kinetic stability along both unfolding pathways, which suggests why the hierarchy of
unfolding rates of titin domains at 0 M denaturant
is reflected in their resistance to force. Thus, while
AFM is essential to allow us to probe the mechanical unfolding pathway, “bulk solution” studies
may give information on the modular assembly of
a mechanical protein, where the determinants of
kinetic stability are the same for both pathways.
This is unlikely to be the case for all proteins.
Materials and Methods
Construction and purification of proteins
The method of construction, production and purification of multimodular repeats of wild-type TI I27 and
mutants using a custom designed multiple cloning
system has been described: in the final construct, the
domains are linked in tandem with a two-residue linker
(corresponding to the restriction site) separating them.33
All “polyproteins” had two cysteine residues inserted at
the C terminus to facilitate attachment to the AFM stage
and a His6 tag at the N terminus to facilitate purification.
This tag was not removed in our constructs. All proteins
were stored in PBS (10 mM sodium phosphate (pH 7.4),
137 mM NaCl, 2.7 mM KCl) at 4 8C in the presence of
0.1% (w/v) sodium azide.
Stability of the mutants
Conclusion
Our aim has been to characterise all species
along the forced unfolding pathway, combining
AFM, protein engineering and MD simulation to
get a detailed picture with atomic resolution.
Here, we have shown that protein engineering
F-value analysis can be applied directly to AFM
experiments and that, where this analysis is in
agreement with simulation, MD simulations can
be used to describe species along the pathway in
detail (Figure 4). Simulations show that the native
state lengthens slightly (N –C distance) upon application of force, but TI I27 retains essentially the
same structure with nearly all native-state contacts
retained. Next, the A-strand detaches from the
body of the protein and the intermediate is formed.
This intermediate has a structure very similar to
that of the native protein with only the residues
that contact the A-strand directly losing native contacts. The transition state for forced unfolding is
also very native-like. The hydrogen bonds and a
number of side-chain contacts between the A0 and
G-strands and the A –B and E –F loops are broken.
Once the transition state is reached, unfolding
Each mutation was made in a model of the folding
intermediate (with the A-strand deleted, TI I27-A) and
the effect of the mutation on the free energy of unfolding
(DDGD-I) determined by equilibrium denaturation in PBS
at 25 8C using guanidinium chloride as a denaturant as
described.11 We have shown that TI I27 has the same
stability in the polyprotein as an isolated domain, so
that measurements of DDG in the isolated domain are a
reasonable approximation of the effect of the mutation
in the polyprotein.7
AFM
The proteins were adsorbed onto a freshly evaporated
gold surface and excess protein was removed by
thorough washing with PBS. All experiments were
carried out in PBS at ambient temperature (this was
measured to be in the range 20 –25 8C for all
experiments). Force measurements were made with a
Molecular Force Probe (Asylum Research, Santa Barbara,
CA), as described.7 Briefly, the AFM cantilever tip was
used to pick up the N-terminal end of the protein by
non-specific adhesion, and then retracted from the surface at a constant speed, measuring the force exerted by
the polyprotein in the process. A range of pulling speeds
between 100 nm s21 and 5000 nm s21 was used (in order
to obtain kinetic information; see below). Silicon nitride
cantilevers (Thermomicroscopes, Sunnyvale CA) with a
876
spring constant of , 0.03 N m21 were used and calibrated using the method implemented in the MFP software. In this, the spring constant is found from the
response of the cantilever to background “white”
noise.34 The criteria for selecting force-extension traces
have been described.23 These are aimed at eliminating
unusual traces that might arise, for example, from two
proteins becoming attached to the cantilever. Typically, a
trace from a single polyprotein gives rise to a number of
sudden rupture events (with a peak force at the point at
which rupture occurs), one for the cooperative unfolding
of each module. The unfolding force is defined to be the
maximum force at the peak immediately before each
unfolding event. All peaks from acceptable traces were
used to determine the unfolding force at a given pulling
speed, using the Igor software (Wavemetrics, Lake
Oswego, OR) of the MFP. At least 40 peaks were counted
at any given pulling speed to determine a mean unfolding force and at least two (usually three) repeat experiments were carried out at each pulling speed. The mean
of the means of experiments carried out on different
days with different cantilevers is shown in Figure 3. The
motivation for this is to reduce the effect of systematic
errors in spring constant calibration.
Mechanical Unfolding of Titin
described in full elsewhere.36 Briefly, to unfold the protein, a constant force is applied parallel with the reaction
co-ordinate, the distance between the N and C termini
(rNC). Nine simulations were performed, three at each of
three different forces (300, 350 and 400 pN). The
CHARMM program37 and potential38 were used with
continuum representation of the solvent.39
To calculate F-values from the simulation, an all-sidechain definition is used, where F is the fraction of native
contacts formed by that side-chain.24 This can be used to
analyse a single structure or an ensemble of structures.
Acknowledgements
We thank Professor Martin Karplus for helpful
discussion. This work was supported by the
Wellcome Trust and the MRC. J.C. is a Wellcome
Trust Senior Research Fellow; R.B.B. is supported
by the Cambridge Commonwealth Trust.
Analysis of AFM data
The dependence of unfolding force on pulling speed
was used to determine the unfolding kinetics using a
simple two-state model (representing unfolding from I
to D).35 The model describes the unfolding energy barrier
by an extrapolated unfolding rate at zero force, k0u , and a
distance from the native state to the transition state, xu.
The value of xu is (inversely) related to the slopes of the
plots in Figure 3 and k0u to the intercepts. A Monte Carlo
simulation approach11,35 was used to solve for the parameters that best describe the data, taking into account
the non-linear loading of the folded modules due to
the elasticity of the unfolded protein: this was modelled
by a worm-like chain model with parameters
obtained from fits to the actual force-extension traces
(the persistence length, a measure of the backbone
flexibility, was 0.35 nm).
F-Value analysis21
For mutants with the same dependence of the force on
the pulling speed as wild-type (all except V86A), F was
calculated directly at a pulling speed of 500 nm s21 (as
judged from individual fits of the force versus pulling
speed dependence):
wt ku
DFxu A ¼ 2RT ln mut
¼ DDG‡-I
ð4Þ
ku
where A is Avogadro’s number.
We have shown that, since the forced unfolding
pathway involves an intermediate, a three-state analysis
is formally more correct to determine absolute values of
kI!‡ and xI!‡.10 However, since we are comparing wildtype and mutants, which have the same unfolding
mechanism, we have used a two-state analysis as
described,21 which is simpler and gives exactly the same
results.
Molecular dynamics simulations
The simulations analysed here have been described in
detail previously17 and the method used has been
References
1. Rief, M., Gautel, M., Oesterhelt, F., Fernandez, J. M.
& Gaub, H. E. (1997). Reversible unfolding of
individual titin immunoglobulin domains by AFM.
Science, 276, 1109– 1112.
2. Rief, M., Gautel, M., Schemmel, A. & Gaub, H. E.
(1998). The mechanical stability of immunoglobulin
and fibronectin III domains in the muscle protein
titin measured by atomic force microscopy. Biophys.
J. 75, 3008–3014.
3. Rief, M., Pascual, J., Saraste, M. & Gaub, H. E. (1999).
Single molecule force spectroscopy of spectrin
repeats: low unfolding forces in helix bundles. J. Mol.
Biol. 286, 553– 561.
4. 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.
5. Oberdorfer, Y., Fuchs, H. & Janshoff, A. (2000). Conformational analysis of native fibronectin by means
of force spectroscopy. Langmuir, 16, 9955– 9958.
6. Carrion-Vazquez, M., Oberhauser, A. F., Fisher, T. E.,
Marszalek, P. E., Li, H. B. & Fernandez, J. M. (2000).
Mechanical design of proteins-studied by singlemolecule force spectroscopy and protein engineering. Prog. Biophys. Mol. Biol. 74, 63– 91.
7. Best, R. B., Li, B., Steward, A., Daggett, V. & Clarke, J.
(2001). Can non-mechanical proteins withstand
force? Stretching barnase by atomic force microscopy
and molecular dynamics simulation. Biophys. J. 81,
2344– 2356.
8. Yang, G., Cecconi, C., Baase, W. A., Vetter, I. R.,
Breyer, W. A., Haack, J. A., Matthews, B. W. et al.
(2000). Solid-state synthesis and mechanical unfolding of polymers of T4 lysozyme. Proc. Natl Acad. Sci.
USA, 97, 139– 144.
9. Li, H. B., Carrion-Vazquez, M., Oberhauser, A. F.,
Marszalek, P. E. & Fernandez, J. M. (2000). Point
mutations alter the mechanical stability of immunoglobulin modules. Nature Struct. Biol. 7, 1117 – 1120.
10. Williams, P. M., Fowler, S. B., Best, R. B., TocaHerrera, J. L., Scott, K. A., Steward, A. & Clarke, J.
Mechanical Unfolding of Titin
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
(2003). Hidden complexity in the mechanical properties of titin. Nature, 422, 446– 449.
Carrion-Vazquez, M., Oberhauser, A. F., Fowler, S. B.,
Marszalek, P. E., Broedel, S. E., Clarke, J. &
Fernandez, J. M. (1999). Mechanical and chemical
unfolding of a single protein: a comparison. Proc.
Natl Acad. Sci. USA, 96, 3694– 3699.
Marszalek, P. E., Lu, H., Li, H. B., Carrion-Vazquez,
M., Oberhauser, A. F., Schulten, K. & Fernandez,
J. M. (1999). Mechanical unfolding intermediates in
titin modules. Nature, 402, 100– 103.
Lu, H. & Schulten, K. (1999). Steered molecular
dynamics simulation of conformational changes of
immunoglobulin domain I27 interpret atomic force
microscopy observations. Chem. Phys. 247, 141– 153.
Lu, H. & Schulten, K. (2000). The key event in forceinduced unfolding of titin’s immunoglobulin
domains. Biophys. J. 79, 51 – 65.
Oberhauser, A. F., Marszalek, P. E., Carrion-Vazquez,
M. & Fernandez, J. M. (1999). Single protein misfolding events captured by atomic force microscopy.
Nature Struct. Biol. 6, 1025– 1028.
Lu, H., Isralewitz, B., Krammer, A., Vogel, V. &
Schulten, K. (1998). Unfolding of titin immunoglobulin domains by steered molecular dynamics
simulation. Biophys. J. 75, 662– 671.
Fowler, S. B., Best, R. B., Toca-Herrera, J. L.,
Rutherford, T. J., Steward, A., Paci, E., Karplus, K. &
Clarke, J. (2002). Mechanical unfolding of a titin Ig
domain: (1) structure of unfolding intermediate
revealed by combining molecular dynamic
simulations, NMR and protein engineering. J. Mol.
Biol. 322, 841– 849.
Brockwell, D. J., Beddard, G. S., Clarkson, J., Zinober,
R. C., Blake, A. W., Trinick, J. et al. (2002). The effect
of core destabilisation on the mechanical resistance
of I27. Biophys. J. 83, 458–472.
Zinober, R. C., Brockwell, D. J., Beddard, G. S., Blake,
A. W., Olmsted, P. D., Radford, S. E. & Smith, D. A.
(2002). Mechanically unfolding proteins: the effect of
unfolding history and the supramolecular scaffold.
Protein Sci. 22, 2759– 2765.
Klimov, D. K. & Thirumalai, D. (2000). Native topology determines force induced unfolding pathways
in globular proteins. Proc. Natl Acad. Sci. USA, 97,
7254–7259.
Best, R. B., Fowler, S. B., Toca-Herrera, J. L. & Clarke,
J. (2002). A simple method for probing the mechanical unfolding pathway of proteins in detail. Proc.
Natl Acad. Sci. USA, 99, 12143– 12148.
Fowler, S. B. & Clarke, J. (2001). Mapping the folding
pathway of an immunoglobulin domain: structural
detail from phi value analysis and movement of the
transition state. Structure, 9, 355– 366.
Best, R. B., Brockwell, D. J., Toca-Herrera, J. L., Blake,
A. W., Smith, D. A., Radford, S. E. & Clarke, J. (2003).
Force mode AFM as a tool for protein folding
studies. Anal. Chim. Acta, 479, 87– 105.
Paci, E., Vendruscolo, M. & Karplus, M. (2002).
Native and non-native interactions along protein
folding and unfolding pathways. Proteins: Struct.
Funct. Genet. 47, 379– 392.
877
25. Fersht, A. R., Matouschek, A. & Serrano, L. (1992).
The folding of an enzyme. I. Theory of protein
engineering analysis of stability and pathway of
protein folding. J. Mol. Biol. 224, 771–782.
26. Paci, E. & Karplus, M. (1999). Forced unfolding of
fibronectin type 3 modules: an analysis by biased
molecular dynamics simulations. J. Mol. Biol. 288,
441 –459.
27. Li, H., Oberhauser, A. F., Fowler, S. B., Clarke, J. &
Fernandez, J. M. (2000). Atomic force microscopy
reveals the mechanical design of a modular protein.
Proc. Natl Acad. Sci. USA, 92, 6527– 6531.
28. Li, H. B., Linke, W. A., Oberhauser, A. F., CarrionVazquez, M., Kerkviliet, J. G., Lu, H. et al. (2002).
Reverse engineering of the giant muscle protein
titin. Nature, 998– 1002.
29. Scott, K. A., Steward, A., Fowler, S. B. & Clarke, J.
(2002). Titin; a multidomain protein that behaves as
the sum of its parts. J. Mol. Biol. 315, 819– 829.
30. Lorch, M., Mason, J. M., Clarke, A. R. & Parker, M. J.
(1999). Effects of core mutations on the folding of a
beta-sheet protein: implications for backbone
organization in the I-State. Biochemistry, 38,
1377 –1385.
31. Hamill, S. J., Steward, A. & Clarke, J. (2000). The
folding of an immunoglobulin-like Greek key protein
is defined by a common-core nucleus and regions
constrained by topology. J. Mol. Biol. 297, 165– 178.
32. Cota, E., Steward, A., Fowler, S. B. & Clarke, J. (2001).
The folding nucleus of a fibronectin type III domain
is composed of core residues of the conserved
immunoglobulin-like fold. J. Mol. Biol. 305, 1185–1197.
33. Steward, A., Toca-Herrera, J. L. & Clarke, J. (2002).
Versatile cloning system for construction of multimeric proteins for use in atomic force microscopy.
Protein Sci. 11, 2179– 2183.
34. Hutter, J. L. & Bechhoefer, J. (1993). Calibration of
atomic force microscope tips. Rev. Sci. Instrum. 64,
1868 –1873.
35. Rief, M., Fernandez, J. M. & Gaub, H. E. (1998).
Elastically coupled two-level systems as a model for
biopolymer extensibility. Phys. Rev. Letters, 81,
4764 –4767.
36. Paci, E. & Karplus, M. (2000). Unfolding proteins by
external forces and temperature: the importance of
topology and energetics. Proc. Natl Acad. Sci. USA,
97, 6521– 6526.
37. Brooks, B. R., Bruccoleri, R. E., Olafson, B. D., States,
D. J., Swaminathan, S. & Karplus, M. (1983).
CHARMM—a program for macromolecular energy
minimization and dynamics calculations. J. Comput.
Chem. 4, 187– 217.
38. Neria, E., Fischer, S. & Karplus, M. (1996). Simulation
of activation free energies in molecular systems.
J. Chem. Phys. 105, 1902–1921.
39. Lazaridis, T. & Karplus, M. (1999). Effective energy
function for proteins in solution. Proteins: Struct.
Funct. Genet. 35, 133– 152.
40. Fersht, A. R. (1998). Structure and Mechanism in
Protein Science: A Guide to Enzyme Catalysis and
Protein Folding, Freeman, New York.
Edited by C. R. Matthews
(Received 18 February 2003; received in revised form 8 May 2003; accepted 8 May 2003)