Folding and unfolding of a photoswitchable peptide from picoseconds to microseconds
Janne A. Ihalainen, Jens Bredenbeck, Rolf Pfister, Jan Helbing, Lei Chi, Ivo H. M. van Stokkum,
G. Andrew Woolley, and Peter Hamm
PNAS published online Mar 19, 2007;
doi:10.1073/pnas.0607748104
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Notes:
Folding and unfolding of a photoswitchable peptide
from picoseconds to microseconds
Janne A. Ihalainen*, Jens Bredenbeck*, Rolf Pfister*, Jan Helbing*, Lei Chi†, Ivo H. M. van Stokkum‡,
G. Andrew Woolley†, and Peter Hamm*§
*Physikalisch-Chemisches Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland; †Department of Chemistry,
University of Toronto, 80 Saint George Street, Toronto M5S 3H6, Canada; ‡Faculty of Sciences, Department of Physics and Astronomy,
Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
Using time-resolved IR spectroscopy, we monitored the kinetics of
folding and unfolding processes of a photoswitchable 16-residue
alanine-based ␣-helical peptide on a timescale from few picoseconds to almost 40 ␮s and over a large temperature range (279 –318
K). The folding and unfolding processes were triggered by an
ultrafast laser pulse that isomerized the cross linker within a few
picoseconds. The main folding and unfolding times (700 ns and 150
ns, respectively, at room temperature) are in line with previous
T-jump experiments obtained from similar peptides. However,
both processes show complex, strongly temperature-dependent
spectral kinetics that deviate clearly from a single-exponential
behavior. Whereas in the unfolding experiment the ensemble
starts from a well defined folded state, the starting ensemble in the
folding experiment is more heterogeneous, which leads to distinctly different kinetics of the experiments, because they are
sensitive to different regions of the energy surface. A qualitative
agreement with the experimental data-set can be obtained by a
model where the unfolded states act as a hub connected to several
separated ‘‘misfolded’’ states with a distribution of rates. We
conclude that a rather large spread of rates (k1 : kn ⬇ 9) is needed
to explain the experimentally observed stretched exponential
response with stretching factor ␤ ⴝ 0.8 at 279 K.
P
rotein relaxation and protein folding kinetics are in many
cases extremely complex processes, mainly because of the
large distribution of the time scales of processes (1). This
complexity often results in nonexponential kinetics and leads to
the kinetics depending on the monitored observable (2–5).
Because of their relatively fast folding times and plainness, a
large amount of work has been concentrated on ␣-helix formation of Ala-rich model peptides with strong helix-propensity
(6–8). Because the ␣-helix is one of the predominant secondary
structures in many proteins and peptides, detailed understanding
of its conformational dynamics can give important insight into
the conformational dynamics of naturally occurring proteins.
Helix dynamics have been studied for the most part by using
laser induced T-jump methods to perturb the equilibrium, and
the subsequent conformational dynamics are detected either by
time-resolved IR spectroscopy (9–13), by fluorescence (14, 15),
or by Raman scattering techniques (16). It has been established
for some time that helix folding is not a two-state process (17).
The overall relaxation of an ␣-helical peptide after an unfolding
perturbation has been found to occur between 120 ns and 420 ns,
at room temperature (9–12, 14, 15). The folding of an ␣-helix has
been found to occur with a time constant of ⬇1.2 ␮s (13, 18).
However, molecular dynamics simulations suggest that polypeptides can undergo considerable structural changes within 1 ns or
less (19–21). By means of a triplet-triplet-quenching technique,
intramolecular contact formation between side chains and intramolecular chain diffusion of a polypeptide have been observed experimentally to take place in the order of 20 ns (22, 23).
Thus, an ⬇10-ns time resolution (the typical time-resolution of
T-jump experiments) is not necessarily sufficient to resolve these
www.pnas.org兾cgi兾doi兾10.1073兾pnas.0607748104
fast processes taking place during the early phases of a folding
or an unfolding process (7).
To study both folding and unfolding for one and the same
molecule, Woolley and coworkers (24, 25) have designed photoswitchable peptides where a crosslinked photoisomerizable
azobenzene determines the helix propensity of the peptide.
When the crosslinker is attached to two cysteines spaced 11
residues apart, the ␣-helical conformation is stabilized by the
linker in its trans conformation, while in the cis conformation,
the linker considerably diminishes the helicity of the peptide, and
as such, the free energy surfaces of these conformations are
considerable different (See Fig. 1A) (24, 25). Moreover, because
the isomerization of the linker is ultrafast (26), folding and
unfolding can be triggered with high time-resolution (18, 27–29).
The sequence of the peptide, Ac-AACARAAAARAAACRANH2 (hereafter noted as the AARA peptide), is the same as that
used in many T-jump studies (10, 14, 16) but is slightly different
from the one studied in our previous report (18), where additional salt bridges stabilized the helical form.
In an ‘‘energy landscape picture,’’ the aim is to reduce the
overwhelmingly large coordination space, which obviously exist
in protein dynamics, to a few (typically one) representative
reaction coordinates. Along that reaction coordinate, a free
energy surface can be established to account for the thermodynamics, and at the same time one is hoping that kinetics can also
be modeled by using some diffusion process on that surface
(30–33). Conceptually, the first step is always possible whether
a ‘‘good’’ or ‘‘bad’’ reaction coordinate has been chosen, but the
second step is problematic and depends on the choice of the
reaction coordinate (34, 35).
T-jump experiments have often been modeled by ‘‘initiation–
propagation models’’ (or the kinetic zipper model) (5, 14, 36).
Each residue of the polypeptide chain is considered to exist in
one of two possible configurations [coil-like (c) or helical-like
(h)] the latter having lower entropy because of the smaller
number of possible conformations. Although this type of analysis
successfully describes a large number of helix relaxation data, the
initiation-propagation model has a tendency to predict compressed rather than stretched exponential kinetics in the folding
direction (14, 33), which contradicts the results of our experiments (this study and ref. 18). Moreover, molecular dynamic
simulations of small peptides (37–41), consistently demonstrate
the existence of low free energy traps in the unfolded state that
are mostly due to nonnative hydrogen bonds. This idea has
recently been supported by UV resonance Raman experiments,
Author contributions: J.A.I., J.B., J.H., G.A.W., and P.H. designed research; J.A.I., J.B., R.P.,
J.H., L.C., G.A.W., and P.H. performed research; R.P., L.C., and G.A.W. contributed new
reagents/analytic tools; J.A.I., J.B., I.H.M.v.S., and P.H. analyzed data; and J.A.I., G.A.W., and
P.H. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS direct submission.
§To
whom correspondence should be addressed. E-mail: p.hamm@pci.unizh.ch.
© 2007 by The National Academy of Sciences of the USA
PNAS 兩 March 27, 2007 兩 vol. 104 兩 no. 13 兩 5383–5388
BIOPHYSICS
Edited by William A. Eaton, National Institutes of Health, Bethesda, MD, and approved January 2, 2007 (received for review September 6, 2006)
Unfolding
430 nm
Folding
1600
1650
1.0
0.03 ns
1 ns
45 ns
141 ns
3600 ns
FTIR
A
0.5
∆Absorption, mOD
Cis
Trans
C
366 nm
Absorption
B
∆ Absorption
A
-0.5
0.4
1700
Energy, 1/cm
Fig. 1. Photoswitchable peptide and its steady-state CAO absorption spectrum. (A) Schematic models of the cis (Upper) and trans (Bottom) peptides,
illustrating the conformational transition induced by the photoswitchable
linker. Hydrogens and side chains are omitted for clarity. (B) FTIR absorbance
spectrum of the peptide in the trans (solid line) and cis (dashed line) states. The
cis spectrum was constructed by using the trans spectrum and the cis–trans
difference spectrum assuming 65% conversion to the cis form [estimation
from the UV-visible absorbance difference (data not shown)]. (C) FTIR difference spectrum of the peptide under 436-nm (trans ⫺ cis, solid line) or 365-nm
irradiation (cis ⫺ trans, dashed line) at room temperature. The FTIR difference
spectra of the crosslinker under the same irradiation conditions are shown as
a dotted line (trans ⫺ cis) and a dash-dotted line (cis ⫺ trans).
which suggested that, e.g., 310 helices might act as traps as well,
in particular for low temperatures (42). Such misfolded traps are
completely ignored in initiation–propagation models. However,
if these misfolded traps turn out to be rate limiting, and neither
initiation nor propagation of the helix itself, then the number of
native contacts will no longer be a good reaction coordinate that
can be used to describe the kinetics of folding.
We demonstrate in this study that detecting both folding and
unfolding processes of an ␣-helix over a large range of temperatures and a wide span of time (from ⬇30 ps up to 36 ␮s) permits
a more detailed discussion of the energy landscapes of both the
folded and unfolded states.
0.0
Folding
B
0.0
-0.4
1560
0.03 ns
0.07 ns
2 ns
50 ns
696 ns
FTIR
Unfolding
1600 1640 1680
Energy, 1/cm
Fig. 2. Time-resolved IR-spectra of the folding and unfolding processes at
room temperature. (A) Transient absorption signal after 425-nm excitation,
which corresponds to the spectral dynamics of the folding process of the
␣-helix. (B) Transient absorption signal after 380-nm excitation, which corresponds to the spectral dynamics of the unfolding process of the ␣-helix. The
D2O heat signal is subtracted from the spectra. The FTIR difference spectrum
(dashed lines; compare Fig. 1C) are scaled for better comparison. The arrows
indicate the direction of the spectral evolution.
nm, respectively, are shown in Fig. 1C. As observed in many
other spectroscopic studies (9–13, 18, 44), the amide I⬘ mode
shifts to lower frequency in the folded conformation, and
therefore the absorption difference spectrum shows a positive
signal ⬇1,633 cm⫺1 and negative signals ⬇1,655 cm⫺1 and 1,680
cm⫺1 (solid line). Indeed, the crosslinker increases considerably
the helix propensity in its trans state (24, 25), as is demonstrated
by CD measurements (Table 1). The perfect mirror symmetry of
the folding and unfolding FTIR difference spectra demonstrates
the reversibility of the processes.
Results
Time Evolution of the IR Spectra. Overall, the spectral dynamics of
Steady-State IR Spectroscopy. Throughout this article, conforma-
the folding process triggered by 425 nm excitation of the
molecules in the cis state closely resemble the results reported in
ref. 18 (Fig. 2A). The early signals up to 30 ps are omitted,
because they are dominated by the response of the linker, which
is heated by absorption of the UV photon and subsequent
ultrafast electronic relaxation of the azobenzene moiety (18, 45).
The first signal that can be unambiguously assigned to the
dynamics of the peptide is seen as a broad bleach at the position
of the amide I⬘ band ⬇30 ps after the laser flash (Fig. 2 A, cyan
tional changes of the peptide are followed by detecting changes
of the amide I⬘ band (CAO stretch), because this band is very
sensitive to transition dipole coupling effects and to the Hbonding of the CAO-group (43). The absorption spectra of the
crosslinked AARA peptide in its trans state and in its cis state
are shown in Fig. 1B. The FTIR difference spectra between the
folded conformation (trans state) and unfolded conformation
(cis state), measured under illumination either at 435 nm or 365
Table 1. Helicities, folding times, and unfolding times of the photoswitchable peptide
Helicity, %
Temp., °C
6
12
19
32
45
Folding
Trans
Cis
66
64
60
55
46
20
18
13
10
11
␶f1,
ps
80
120
100
140
140
␶f2,
ns
18
17
15
15
6
Unfolding
␶f3,
ns
␤f3
1,370
1,040
770
430
270
0.80
0.82
0.91
1.0
0.98
Temp., °C
8
19
29
41
␶u1 ,
ps
50
40
30
20
␶u2 , ns
␶u3 , ns
9
5
3
1
370
160
90
50
Helicities in the trans and cis states of the linker are estimated from the CD signal at [␪ ]222 without irradiation (for the trans state) and ⬍365-nm irradiation
(for the cis state). A 65% conversion to the cis form under 365-nm light is used [based on the UV-visible absorbance difference (data not shown)]. The folding
and unfolding times at various temperatures are fitted with three time constants, and in the case of folding, one free stretching factor was used (␤3). The
wavelength-dependent amplitudes of the components at room temperature are shown as decay-associated difference spectra [␧l(␯ )] in Fig. 3. The estimated
error of the analysis is 10% for the CD experiment, 30% for the two first-lifetime components, 10% for ␶3, and 5% for ␤.
5384 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0607748104
Ihalainen et al.
B
A
G
C
εinf.
Normalized ∆OD
Folding
ε1
0
o
-1
1
1630 cm
ε2
o
45 C
6C
-1
1657 cm
D
-1
1677 cm
E
-1
H
F
ε3
U nfolding
0
-1
o
1630 cm
-1
0
8C
-1
1
1657 cm
2
10 10 10 10 10
3
Folding
ε1(*0. 5)
ε2
o
41 C
ε3
DADS, a.u.
1
-1
0
-1
1
2
10 10 10 10 10
3
Time, ns
1677 cm
-1
-1
1
0
εinf.
2
10 10 10 10 10
3
1620
U nfolding
1650
1680
Energy, 1/cm
line). This indicates a perturbation of the peptide backbone by
the stretching of the photoswitch in the early times after the
excitation pulse. The broad bleach undergoes a blue shift and
disappears within 45 ns (red and green lines). Then, a spectrum
with a shape similar to the steady-state difference spectrum (Fig.
1C) appears at ⬇140 ns after the laser flash (Fig. 2 A, blue line)
consistent with the formation of the ␣-helix structure. The final
spectrum is obtained after 3.6 ␮s (black line).
Fig. 2B shows the spectral evolution of the unfolding process
triggered by 380 nm excitation of the molecules in the trans state.
The signals due to peptide dynamics are smaller overall in the
unfolding experiment, because the quantum yield of the azo
linked peptide for the trans 3 cis isomerization (0.08) is much
smaller than that of the cis 3 trans isomerization (0.62) (46). The
spectrum at 30 ps after the laser flash is again dominated by
relaxation of the linker, which is seen as negative signals at 1,600
cm⫺1 and 1,670 cm⫺1 and a positive signal at 1,645 cm⫺1 (Fig. 2B,
cyan line). A narrow bleach at ⬇1630 cm⫺1, which reports
perturbations in the peptide, can be observed 70 ps after the laser
flash (red line). The unfolding signal develops further over 2 ns
(green line), and after 50 ns, the signal is more than half-way
complete (blue line), although the spectral shapes between 1,660
cm⫺1 and 1,680 cm⫺1 are still underdeveloped. The final spectrum, which closely resembles the steady-state cis–trans difference spectrum (Fig. 1C), is obtained ⬇700 ns after excitation
(Fig. 2B, black line). Thus, at room temperature, the unfolding
process is about five times faster than the folding process.
Temperature Dependent Amide Iⴕ Dynamics. Fig. 3 shows time traces
at various wavelengths of the amide I⬘ band during the folding
and unfolding processes at various temperatures. Immediate
observations for the folding (Fig. 3 A–H Upper) and unfolding
(Fig. 3 A–H Lower) processes are as follows: (i) a strong
temperature dependence of both processes, (ii) strong nonexponentiality at low temperatures in the folding experiment and
at all temperatures in the unfolding experiment where a clear
biphasic behavior can be observed, and (iii) the spectroscopic
responses are different at different wavelengths, in agreement with earlier observations made by using T-jump experiments (9, 10).
The time traces observed between 1,616 cm⫺1 and 1,717 cm⫺1
were globally fit to
冘
n
␺共t, ␭) ⫽
l⫽1
Ihalainen et al.
␧l(␯)exp关⫺共t/␶l)␤l]
with a common set of time constants, where ␺(t,␭) is the time
resolved spectrum which is a sum of ␧l(␯) spectra (or decay
associated difference spectra) multiplied by exponential decays
with time constants ␶l and stretching factors ␤l. This is a typical
global analysis method (with stretched exponential kinetics) that
takes into account both the spectral information and the temporal behavior of the process in ref. 47. The fitted traces are
shown as solid lines passing through the measured data points
(Fig. 3 A–F). One should note that spectral shifts, which obviously take place in the spectral dynamics of both processes
studied, partially obstruct this type of analysis. The rather large
error margins associated with the first two time constants (␶f1 and
␶2f) in the folding process are due to such spectral shifts but also
due to the small amplitudes of the folding signal. However, by
using a global analysis method, the time scales and the relative
magnitudes of particular spectral ‘‘events’’ become clearly apparent. In the unfolding experiment, the time traces show
multiphasic behavior. In the folding experiment, spectrally distinct kinetics dictate the use of several components (Fig. 3).
Three time constants were found to be required for a satisfactory
fit of the data for both the folding and unfolding processes. In
principle, one should be able to fit a stretching factor for each
component, but the stretching factor could reliably be fitted only
for the main folding phase (␤f3) as a free parameter, because of
its clear spectral and temporal separation from the other components. The fitting parameters are collected in Table 1, and the
wavelength-dependent amplitudes of the components ␧l(␯) at
room temperature are plotted in Fig. 3 G and H. The spectra
␧1(␯) to ␧3(␯) (circles) correspond to the amplitudes of the
change of the signal to the final spectrum ␧inf(␯), which has
infinite lifetime (blue line).
It is obvious that the spectral dynamics are entirely different
in the unfolding process (which is usually studied in T-jump
experiments) from those of the folding process (Figs. 2 and 3).
In the case of folding (Table 1 and Fig. 3G), the first component
shows the blue shift of the broad bleach, observed in the time
evolution of the IR-spectra (see Fig. 2). A further blue-shift and
the disappearance of the broad bleach take place during ␶2f. The
third lifetime corresponds to the main folding phase. The
amplitudes of the first two components are much smaller than
that of the third component and only the third phase shows a
distinct temperature dependence, both in terms of time constant
and the stretching factor (␶3f, and ␤f3, respectively). In the
unfolding process (Table 1 and Fig. 3H), the first time constant
is dominated by the dynamics of the linker, because the signals
from the peptide are much smaller. In contrast to the folding
PNAS 兩 March 27, 2007 兩 vol. 104 兩 no. 13 兩 5385
BIOPHYSICS
Fig. 3. Kinetic traces of folding and unfolding processes. (A–F) Dynamic helix folding (A–C) and unfolding (D–F) signals at various temperatures (black, lowest
temperature; blue, highest temperature) observed at 1,630 cm⫺1, 1,657 cm⫺1, and at 1,677 cm⫺1. The traces are normalized to their maxima for better comparison.
The data are shown as circles, and the fits are shown as solid lines. (G and H) Room temperature decay-associated difference spectra of the folding and the
unfolding processes. The infinitely long component is shown as a blue line.
A
Lo g 10k [ s-1]
Unfolding
7.0
T4
T5
T3
T3
6.5
6.0
B
T4
T5
U
U
F
F
Folding
T2
T1
3.2
3.4
1000/ T
C
Discussion
It has been argued that the trans state of the linker stabilizes the
␣-helix structure but does not force the molecule into this
secondary structure (18). In the early phase of the folding
process the spectral responses in the amide I⬘ difference signal
are relatively minor compared with the overall signal. The broad
bleach ⬇1,630 cm⫺1, observed ⬇30 ps after initiation of the
folding process (Fig. 2 A), suggests that a number of (native or
nonnative) hydrogen bonds responsible for the small helicity in
the cis conformation break because of the isomerization of the
linker. However, the conformational space of the initial state in
the unfolding experiment is much narrower (see Fig. 1 A),
especially at low temperatures, and therefore the isomerization
of the linker can be expected to rapidly lead to large changes in
the peptide. Although the signal from the linker itself is dominant in the unfolding experiment, the effects of the isomerization
of the linker on the peptide are observable as a narrow bleach
at 1,630 cm⫺1 as early as 70 ps after the laser flash, indicating an
immediate breakage of almost one-third of the (native) H-bonds.
The amplitude (Fig. 3D) of this phase indicates that a larger
number of hydrogen bonds are broken at lower temperatures,
consistent with the larger helicity of the peptide at lower
temperatures (Table 1). However, although a considerable fraction of the response of the unfolded state occurs on a picosecond
timescale (up to 2 ns), further unfolding processes take place up
to a few hundreds ns. The unfolding behavior of the peptide
observed during this time is similar to that observed in T-jump
experiments on closely related peptides (9–13), suggesting that
our molecule behaves in a way similar to unlinked ␣-helices.
Although one should keep in mind that the photoswitch might
reduce the accessible configuration space, the molecule still
shows much of the complexity of protein folding.
In agreement with earlier studies (9, 10, 13, 14, 18), we find
that the folding and unfolding of an ␣-helix are strongly thermally activated (Figs. 3 and 4). From the slopes of the logarithmic
rate constant as a function of reciprocal temperature (Fig. 4),
one would conclude that a large enthalpic barrier exists between
folded and unfolded states (31 kJ/mol for folding and 37 kJ/mol
for unfolding). In a two-state picture, such a high barrier would
lead to single-exponential kinetics, in clear contradiction to the
experimentally observed nonexponential response.
In our previous study we resolved the conflict between a high
apparent folding barrier on the one hand and nonexponential
D
U
kt
T1-T5
experiment, the transient signal during the subsequent 10 ns of
the unfolding process shows clear absorption changes, a considerable decay amplitude [␧2(␯) in Fig. 3H], and a clear temperature dependence. The final part of the unfolding process takes
place in the 100-ns range [␧3(␯) in Fig. 3H). All time components
are strongly temperature-dependent (Table 1).
HU
HU
-TSU
Fig. 4. Logarithmic folding and unfolding rates as a mean decay rate at
various temperatures estimated from the integrated area under the normalized signal at 1,630 cm⫺1 and at 1,677 cm⫺1 for folding and unfolding,
respectively.
5386 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0607748104
T2
T1
3.6
-TSU
kf
kf
F
T1-T5
kt
U
F
Fig. 5. Kinetic model. Kinetic scheme connecting the folded state (F) with a
few traps (T1-T5) through an ensemble of unfolded states (U) in a star-like
manner. The thickness of the arrows connecting the states symbolize a distribution of rates. (A and B) Shown are the population flow in folding (A) and
unfolding (B) experiments, respectively. (C and D) Energetics of the relevant
states at low (C) and high (D) temperatures.
kinectics on the other hand by introducing a diffusive process on
a relatively shallow one-dimensional free energy surface (18). In
this case, the temperature dependence would be governed by a
super-Arrhenius law (48); that is, by many but much smaller
barriers on a rugged energy surface. Initiation–propagation
models, in contrast, would provide a reasonable fit for the
unfolding experiment for any given temperature.
However, without adding a strongly temperature-dependent
diffusion constant to the model (with a variation that exceeds
that expected because of the change of solvent viscosity),
initiation–propagation models cannot resolve the conflict between apparent high activation barrier and nonexponential
kinetics (15). This is because the free energy surface consists of
two wells, i.e., effectively a two-state systems, except when the
barrier is in the range of kBT or smaller [which is the case when
a double (31) or multiple (33) sequence approach is used].
Furthermore, as discussed in detail and on quite general grounds
in ref. 33, initiation–propagation models (as well as downhill
folding models) have the tendency to produce compressed rather
than stretched exponential kinetics for the folding direction,
where the ensemble is approaching the state the spectroscopic
observable is most sensitive to. In fact, compressed kinetics has
been predicted already quite some time ago for the folding
direction (see figure 10 of ref. 14) but remained undiscussed.
All these models have in common that they try to reduce the
kinetics onto a one-dimensional free energy surface. In this case,
the total of all experimental observations (i.e., folding and
unfolding kinetics of one and the same molecule including all
relevant timescales from picoseconds to microseconds and in a
large temperature range) render constraints on the nature of the
free energy surface that are difficult to resolve. If, however, one
gives up the assumption of diffusion on a one-dimentional
surface, the constraints are significantly less. Indeed, in network
analyses of the folding of similarly small peptides, it has been
argued that the conformational ensemble of small peptides in
solution is composed of relatively few clusters of states (40, 41,
39, 49), comprising the native (folded) state and misfolded states
trapped by nonnative hydrogen bonds and potentially saltbridges. The network analysis furthermore suggests that one
misfolded state can transfer into another misfolded state only
through a hub, whereas the direct transfer between misfolded
states is significantly slower (40). Reducing these ideas to a
Ihalainen et al.
Ihalainen et al.
coincide with reported values of the folding speed limit. In
agreement with experiment, the transition between nonexponential and exponential kinetics will occur in the same temperature regime as the shift of the equilibrium constant, because the
temperature variation of the unfolded state U is responsible for
both effects.
If one were to combine all misfolded traps Ti together with the
unfolded ensemble U into one thermodynamic state, that state
would be entropically lowered, and one could regain an initiation–propagation model. From the perspective of thermodynamics, this is, of course, possible. From the perspective of kinetics,
however, such an unification is meaningful only if the foldingrate kt were the rate limiting step. In this case, however, a
two-state model would effectively be recovered, leaving us again
with the conflict between high apparent folding barrier and
nonexponential kinetics. Similarly, if the traps were connected
among each other directly by fast rates, and not through a hub,
one could again unify them, still yielding the inconsistency of a
one-dimensional reaction coordinate. Hence, within the framework of the star-like model Fig. 5, we can indeed provide
experimental validation to the theoretical suggestion of the
existence of a hub for folding (40). The hub would be the
unfolded state U, but because that is coupled to the folded state
F in a non-rate-limiting manner, the latter would effectively be
a hub as well (40).
Conclusion
In a one-dimensional diffusion model, the total of all experimental observations renders constraints on the nature of the free
energy surface that are difficult to solve and tend to produce
contradictions in terms. These problems disappear when giving
up the one-dimensional assumption. However, it should be
stressed that the problem is highly underdetermined experimentally, and current experiments do not allow one to uniquely
resolve it. Only all-atom molecular dynamics simulations can
provide the information content sufficient to distill out physical
pictures. The set of experimental data presented here is more
complete than any experiment so far, and sets clear benchmarks
for comparison with computational results. To summarize our
key observations: (i) both folding and unfolding show complex
spectral kinetics at all time ranges from picoseconds up to
microseconds, (ii) the kinetics of both folding and unfolding
processes show strong temperature dependence, (iii) different
types of kinetics are obtained when one observes folding or
unfolding process at different wavelengths within the amide I⬘
band, (iv) the spectral responses are different in the folding and
unfolding experiments, and finally (v) the whole data set can be
expressed with a rather simple star-like model. All this has been
observed for one molecule. Molecular dynamics simulations of
a photoswitchable helical peptide are helical peptide are currently underway to investigate the kinetics at a atomic level of
detail and compare them with our experimental data.
Materials and Methods
Peptide Synthesis. The 16-residue peptide was prepared by using
Fmoc-based solid phase peptide synthesis methods (25) (JPT
Peptide Technologies, Berlin, Germany). The two cysteine residues were crosslinked with the photoisomerizable linker according to refs. 24 and 25 to obtain the photoswitchable AARA
peptide. For the spectroscopic experiments, TFA was removed
by liquid chromatography (Bond Elut SAX; Varian, Palo Alto,
CA) columns rinsed with H2O, 10 mM phosphate buffer, and 1
mM HCl.
Steady-State IR and CD Measurements. The desired state of the
photoswitch was obtained by properly filtered high-power Hg
light before taking IR and CD spectra in FTS 175C (Bio-Rad,
Cambridge, MA) or Jasco (Gross-Umstadt, Germany) Model
PNAS 兩 March 27, 2007 兩 vol. 104 兩 no. 13 兩 5387
BIOPHYSICS
simple kinetic scheme, one arrives at a model where an ensemble
of unfolded states U is connected to a set of misfolded traps in
a star-like manner (Fig. 5). Here, we discuss to what extent such
a scenario can account for our experimental findings.
In the folding experiment (Fig. 5A), all traps are initially
populated and feed into the folded states (F) through the
unfolded ensemble U. The response, therefore, will be a relatively nonspecific sum of all contributions that results in
stretched exponential relaxation provided the individual rates kt,
are all different. Solving a system of rate equations according to
Fig. 5A with equally distributed barrier heights (assuming that
the folding rate kt is not rate limiting, see below) shows that a
spread of rates ⬇9 is required to obtain a stretching factor of ␤ ⫽
0.8 (a spread of ⬇20 is needed for the larger stretching factor ␤ ⫽
0.7 in ref. 18). Thus, although a stretching factor of ␤ ⫽ 0.8
appears to be a relatively small deviation from exponential
behavior, it can be the result of dramatic effects on a microscopic
level (50).
In the unfolding experiment (Fig. 5B), in contrast, the process
starts from the better defined folded state F. Initially, it will feed
only into kinetically favored states (Fig. 5B, T1). Only after
longer times will thermodynamic equilibrium be achieved, which
may even disfavor the kinetically favored states. In an unfolding
experiment, the ensemble of trajectories will initially be much
more focused than in the folding experiment, because it starts
from a defined state F, rather than from a broad distribution of
states. In other words, the ensemble of trajectories will initially
follow a relatively specific pathway. This is in qualitative agreement with a number of experimental observations: the distinct
biphasic kinetics (Fig. 3E), the large amplitude ␧2(␯) observed in
the early phase of the unfolding experiment (Fig. 3H), and the
stronger wavelength dependence in the unfolding experiment
(Fig. 3 E and F versus Fig. 3 B and C). In fact, solving a rate
equation system according to the model in Fig. 5B leads to two
distinct timescales for the unfolding experiment. Hence, the
counterpart to the stretched exponential response in the folding
experiment (component ␶3f in Table 1) is the biphasic response
in the unfolding experiment with two distinct timescales (components ␶u2 and ␶u3 in Table 1). Component ␶2f is negligibly small
in the folding experiment (Fig. 3G). Solving the same system of
rate equations furthermore suggests that the ratio of folding
versus unfolding rates is a qualitative measure of the number of
accessible traps (if one assumes that the photoswitch modifies
the energetics of the folded state solely, and not that of any
barrier relative to the traps). As we observe a value of ⬇5 for that
ratio experimentally, we conclude that indeed only relatively few
such traps exist. In part, this might be due to the photoswitch that
reduces the accessible configuration space of the molecule.
The average rate increases with temperature and at the same
time the nonexponential response disappears (Table 1). In the
framework of the model discussed here, this can be understood
as follows: The unfolded ensemble U is the one with the highest
entropy (because, as open structure it has the largest conformational space) and the highest enthalpy (because hydrogenbonds are missing). As such, its free energy varies strongest with
temperature, such that it might effectively act as a transition state
at low temperatures (Fig. 5C). In this case, the inhomogeneous
distribution of rates between U and the trapped states are
relevant, rendering the overall kinetics nonexponential. At high
temperatures, in contrast, the unfolded state U is lowered,
shifting the equilibrium toward the unfolded state U, away from
both the folded state F and the traps Ti (Fig. 5D). The molecules
that fold directly out of the unfolded state U will lead to
essentially exponential kinetics. Furthermore, the folding barrier
has disappeared, and the individual rates from the traps will
approach the more uniform ‘‘speed limit’’ of folding on an
essentially flat free energy surface (22, 23). In fact, the fastest
time constants we observe in our experiment (␶2 in Table 1)
J-710 spectrometers, respectively. The helix content of both
conformations was estimated from the CD signal at 222 nm as
described in ref. 24.
Time-Resolved IR Spectroscopy. The dissolved sample was circulated
in a closed cycle CaF2 flow cell with a 100-␮m optical pathlength
(51). The closed cycle was thermostated to ⫾1°C. The dark-adapted
AARA peptide is in the trans-azo conformation (ccis ⬍ 1%) (25).
To monitor unfolding, the transition from trans (folded) to cis
(unfolded) was initiated by a short (700-fs) laser pulse at 380 nm.
Between the experiments at different temperatures, the sample was
heated to 318 K in darkness for 30 min to relax the small amount
of molecules (ccis ⬍ 10%) accumulated in the cis conformation back
to trans-azo conformation. To monitor folding, the initial cis state
was prepared by using continuous UV irradiation with an Ar-Ion
Laser (363 nm, 50 mW; Coherent Innova 100, Santa Clara, California). The transition from cis to trans was initiated by a 700-fs
laser pulse at 425 nm.
The evolution of the peptide after photoswitching the linker
was monitored by time resolved IR spectroscopy. A setup
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