12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 1
V12: Folding of Single Proteins
Why study single proteins?
How do proteins spontaneously find their native structure?
Theoretical studies overall downhill funnel-shaped energy surface.
Surface is complex and rugged
folding behavior of individual molecules may differ widely!
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 2
V2: NMR-Daten für Faltung von Lysozym
Man findetzwei Faltungs-pfade. Der gelbe ist schnell,der grüne langsam.
Dobson, Karplus,Angew. ChemieInt. Ed. 37, 868 (1998)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 3
Folding of Single Proteins: experimental realisation
Reversible folding/unfolding transitions of single protein molecules can be studied
at equilibrium.
Choose experimental conditions under which each protein molecules spends (on
average) an equal amount of time on the two sides of the folding barrier.
Monitor e.g. FRET signal between fluorescent probes attached to 2 ends of
molecule.
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 4
Using FRET to Study Folding of Single ProteinsSchematic structures of protein and
polyproline helices labelled with donor (Alexa
488) and acceptor (Alexa 594) dyes.
a, Folded CspTm, a 66-residue, five-stranded
-barrel protein;
b, unfolded CspTm;
c, (Pro)6; and d, (Pro)20 .
A blue laser excites the green-emitting donor
dye, which can transfer excitation energy to
the red-emitting acceptor dye at a rate that
depends on the inverse sixth power of the
interdye distance In each case, the functional
form of the FRET efficiency E versus
distance (blue curve) is shown, as well as a
representation of the probability distribution of
distances between donor and acceptor dyes,
P (red curve). Schuler et al. Nature 419, 743 (2002)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 5
FRET efficiencies for single moleculesDependence of the means and widths of the
measured FRET efficiency (Eapp) on the
concentration of GdmCl.
a, Eapp for (Pro)20.
b , Single molecule mean values (filled
circles), ensemble FRET efficiencies (open
circles), and associated two-state fit
(unbroken curve) for CspTm .
Dotted curve: third-order polynomial fit to the
unfolded protein data that was matched
(dashed curve) to the ensemble data
between 4 and 6 M GdmCl.
Schuler et al. Nature 419, 743 (2002)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 6
Influence of Protein Dynamics on Width
Two limiting cases for polypeptide dynamics in experiments on freely diffusing
molecules. a , If the end-to-end distance of the protein does not change during
the observation period in the illuminated volume (blue), then the distribution of
transfer efficiencies reflects the equilibrium end-to-end distance distribution of the
molecules and consequently results in a very broad probability distribution of
FRET efficiencies, shown here for a gaussian chain (red curve).
b, If the molecule reconfigures fast relative to the time it takes to diffuse through
the illuminated volume, then the FRET efficiency averages completely and is the
same for every molecule. Schuler et al. Nature 419, 743 (2002)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 7
Estimate folding barrier
Upper limit for reconfiguration time in unfolded state: 0 = 25 s.
Ensemble folding time 12 ms.
Use Kramers equation
kT
Gf exp2
max
0min
Lower limit for free energy barrier of folding: 4 kT.
Upper bound: reconfiguration time of gaussian chain: 11 kT
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 8
Limitation of previous study
Free diffusion experiments can only be used to examine states that are
substantially populated at equilibrium.
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 9
Folding Studies near Native ConditionsMicrofluidic mixer. (A) Channel pattern
and photograph of mixing region as
seen through the microscope objective
and bonded coverslip. Solutions
containing protein, denaturant, and
buffer were driven through the
channels with compressed air. Arrows
indicate the direction of flow.
(B) View of the mixing region.
Computed denaturant concentration is
indicated by color. The laser beam
(light blue) and collected fluorescence
(yellow) are shown 100 µm from the
center inlet.
Lipman et al. Science 301, 1233 (2002)
(C) Cross section of the mixing region.
Actual measurements were made at
distances 100 µm from the center inlet
channel. Because the flow velocity at the
vertical center of the observation channel
is about 1 µm ms-1, this corresponds to
times 0.1 s.
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 10
Folding of Membrane Proteins
(A) Histograms of measured FRET efficiency, Em, during folding. (Top) The Em
distribution at equilibrium before mixing. The vertical redline indicates the mean
value for Em in the unfolded state after mixing. Measurements of Em were taken
(typically for 30 minutes) at various distances from the mixing region and thus at
various times after the change in GdmCl concentration.
(B) Comparison of single-molecule and ensemble folding kinetics. The decrease
in donor fluorescence from stopped-flow experiments is shown in green. Single-
molecule data are represented by filled circles, with a corresponding single
exponential fit (black). The fit to the single-molecule data has a rate constant of
6.6 ± 0.8 s-1, in agreement with the result from ensemble measurements (5.7 ±
0.4 s-1). Lipman et al. Science 301, 1233 (2002)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 11
Unfolding of CspTM in GdmClDependence of (A) the mean values
and (B) peak widths () of Em
histograms for unfolded Csp as a
function of GdmCl concentration. Peak
widths are standard deviations of
Gaussian fits.
The colored region indicates the range
of denaturant concentrations where
reliable data cannot be obtained from
corresponding equilibrium experiments.
even though there is significant
compactification of U between 6 M and
0.5 M GdmCl, there is no increase in
the reconfiguration time. Schuler et al. Nature 419, 743 (2002)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 12
Folding of single adenylate kinase molecules
Challenges of studies on single molecules:
find a way to restrict the molecules spatially
such that temporal folding trajectories can be
measured without modifying the
conformational dynamics of the protein.
- such modification may result e.g. from
immobilizing the protein on a surface.
- technique used here: trap single molecules in
surface-tethered unilamellar lipid vesicles.
The vesicles ( = 120 nm) are much larger
than the proteins ( = 5 nm) so they allow the
proteins to diffuse freely.
Gilad Haran, Weizman Institute
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 13
Folding of single adenylate kinase (AK) molecules
Ribbon representation of the structure of
AK from E. coli.
Positions 73 and 203 (labeled by
acceptor and donor fluorophores) are
marked with arrows.
Folding behavior of AK:
not a simple two-state folder;
at least one intermediate along folding
path.
Ensemble folding time ca. 4 min.
Rhoades et al. PNAS 100, 3197 (2003)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 14
Verification that AK molecules don’t interact with wall(A and B) Distributions of average fluorescence polarization
values of single AK molecules labeled with the donor only
obtained after excitation with circularly polarized light. The
distribution shown in A is for molecules trapped in vesicles at
0.4 M Gdn•HCl, and the one shown in B is for molecules
adsorbed directly on glass. The very narrow width of the
polarization distributions of vesicle-trapped molecules,
compared with the width of the distribution of glass-adsorbed
molecules, indicates freedom of rotation of the trapped
molecules.
(C) A typical time-dependent fluorescence polarization
trajectory of a single AK molecule labeled with the donor only
and trapped in a lipid vesicle. The vertically polarized (IV) and
horizontally polarized (IH) components of the fluorescence are
shown in gray and black, respectively.
(D) The fluorescence polarization calculated from the data in
C. The lack of any long-term jumps in the polarization
indicates that this protein molecule does not become static
(e.g., due to adsorption on the vesicle wall) for any
considerable amount of time. Rhoades et al. PNAS 100, 3197 (2003)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 15
FRET distributions of AK in vesicles under native and midtransition conditions
(A and B) Distributions of EET values obtained from single-molecule
trajectories of labeled AK molecules trapped in vesicles under native and
denaturing (2 M Gdn•HCl) conditions. The distributions are essentially
unimodal, and their average values, 0.8 and 0.14, are close to the
ensemble values.
(C) Distribution of EET values obtained from single-molecule trajectories of
encapsulated AK molecules prepared in 0.4 M Gdn•HCl (near
midtransition conditions) that showed folding/unfolding transitions.
The distribution can be roughly divided into two subdistributions, one due
to the "denatured" ensemble, with EET values < 0.45, and one due to the
"folded" ensemble, with EET values larger than that value, as illustrated by
the black lines (Gaussian fits). The distribution of FRET efficiencies of all
the trajectories measured for molecules in 0.4 M Gdn•HCl (data not
shown) has peaks at the same values as the distribution made from
molecules that only showed transitions (C), with a greater proportion of the
distribution in the folded ensemble. Additionally, the average value of this
single-molecule distribution (0.6) matches quite well with the measured
ensemble value. Rhoades et al. PNAS 100, 3197 (2003)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 16
Observation of heterogenous folding pathways
(A and C) Time traces of individual
vesicle-trapped AK molecules under
midtransition conditions with the acceptor
signal in red and the donor in green. (B
and D) EET trajectories calculated from the
signals in A and C, respectively.
In A and B several transitions occur
between states that are essentially within
the "folded" ensemble, whereas in C and
D a single transition takes the molecule
from the folded to the "denatured"
ensemble. Note that transitions can be
strictly recognized by an anticorrelated
change in the donor and acceptor
fluorescence intensities as opposed to
uncorrelated fluctuations sometimes
appearing in one of the signals.Rhoades et al. PNAS 100, 3197 (2003)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 17
Characterize folding/unfolding transitions
(A) Map of folding/unfolding transitions obtained from
single-molecule trajectories. Each point represents
the final vs. initial FRET efficiency for one transition.
The line is drawn to distinguish folding and unfolding
transitions; above the line are folding transitions
(efficiency increases), and below the line are
unfolding transitions (efficiency decreases).
(B) Distribution of transition sizes (i.e., final minus
initial efficiencies) as obtained from the map in A.
The two branches of the distribution represent
unfolding and folding transitions, respectively. The
overall similarity of the shape of the two branches
indicates uniform sampling of the energy landscape.
They both peak at a low efficiency value, signifying a
preference for small-step transitions.
Rhoades et al. PNAS 100, 3197 (2003)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 18
Interpretation
- large spread of transitions, can essentially start and end at any value of the FRET
efficiency
- there is a preference for steps that change EET by 0.2-0.3
AK molecules do not typically change from a fully folded to a fully unfolded
conformation in one step. Rather, they jump through several intermediate steps.
Unfortunately, slow folding dynamics of AK does not allow to measure
folding/unfolding times directly from single-molecule trajectories.
Rhoades et al. PNAS 100, 3197 (2003)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 19
Slow Transitions and the Role of Correlated MotionTime-dependent signals from single
molecules showing slow folding or unfolding
transitions. (A) Signals showing a slow folding
transition starting at 0.5 sec and ending at 2
sec. The same signals display a fast unfolding
transition as well (at 3 sec).
(B) EET trajectory calculated from the signals
in A.
(C) The interprobe distance trajectory showing
that the slow transition involves a chain
compaction by only 20%. The distance was
computed from the curve in B by using a
Förster distance (R0) of 49 Å.
(D–F) Additional EET trajectories
demonstrating slow transitions. Rhoades et al. PNAS 100, 3197 (2003)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 20
Interpretation
- In contrast to the fast intrinsic dynamics of the cold-shock protein,
AK molecules show quite slow transitions. A compactation by only 20% may take
as much as 1.5 s.
- occurrence of transitions showing a slow, gradual change of EET indicates
directed motion on energy landscape, possibly slowed down by local traps.
highly correlated, non-Markovian chain dynamics?
slow transition may also be result of slow growth of a folding nucleus
- in the same molecule both fast and slow transitions appear.
The slow transitions are not preceded by a fast jump.
Enthalpic barriers very fast transition/jump, even on single molecule level.
Entropic barriers diffusion through large # of local states
Rhoades et al. PNAS 100, 3197 (2003)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 21
Monitor Folding Trajectories of Single Proteins by AFM
Use single-molecule AFM technique in the „force-clamp“ mode
where a constant force is applied to a single polyprotein
(here: typically nine repeats of ubiquitin).
- monitor probabilistic unfolding of ubiquitin = stepwise elongations
Fernandez and Li, Science 303, 1674 (2004)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 22
Folding pathway of ubiquitin(A) The end-to-end length of a protein as a function of time.
(B) The corresponding applied force as a function of time.
The inset in (A) shows a schematic of the events that occur at
different times during the stretchrelaxation cycle (numbered
from 1 to 5).
zp, piezoelectric actuator displacement;
Lc, contour length.
The length of the protein (in nanometers) evolves in time as it
first extends by unfolding at a constant stretching force of 122
pN. This stage is characterized by step increases in length of
20 nm each, marking each ubiquitin unfolding event,
numbered 1 to 3.
The first unfolding event (1) occurred very close to the
beginning of the recording and therefore it is magnified with a
logarithmic time scale (blue inset) with the length dimension
plotted at half scale. Upon quenching the force to 15 pN, the
protein spontaneously contracted, first in a steplike manner
resulting from the elastic recoil of the unfolded polymer (4),
and then by a continuous collapse as the protein folds (5).
The complex time course of this collapse in the protein’s
length reflects the folding trajectory of ubiquitin at a low
stretching force.
Fernandez and Li, Science 303, 1674 (2004)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 23
Verification
Fernandez and Li, Science 303, 1674 (2004)
To confirm that our polyubiquitin
had indeed folded, at 14 s we
stretched again back to 122 pN (B).
The initial steplike extension is the
elastic stretching of the folded
polyubiquitin.
Afterward, we observed steplike
extension events of 20 nm each,
corresponding to the unfolding of
the ubiquitin proteins that had
previously refolded. After these
unfolding events, the length of the
polyubiquitin is the same as that
measured before the folding cycle
began (3).
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 24
folding includes several discrete processesFolding is characterized by a continuous collapse
rather than by a discrete all-or-none process. (A) and
(B) show typical recordings of the time course of the
spontaneous collapse in the end-to-end length of an
unfolded polyubiquitin, observed after quenching to a
low force.
(A) Four distinct stages can be identified. The first
stage is fast and we interpret it as the elastic recoil of
an ideal polymer chain (see magnified trace in the
top inset).
The next three stages are marked by abrupt changes
in slope and correspond to the folding trajectory of
ubiquitin. These stages can be distinguished by their
different slopes. Stages 2 and 3 always show peak-
to-peak fluctuations in length of several nanometers.
The rapid final contraction of stage 4 marks the end
of the folding event. This final collapse stage is not
instantaneous, as can be seen on the magnified
trace in the lower inset. We measure the total
duration of the collapse, t , from the beginning of the
quench until the end of stage 4.Fernandez and Li, Science 303, 1674 (2004)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 25
Length distribution of protein
(B) The folding collapse is marked by
large fluctuations in the length of the
protein. These fluctuations greatly
diminish in amplitude after folding is
complete. The inset at the top is a record
of the end-to-end fluctuations of the
protein before the quench (region I),
during the folding collapse (region II), and
after folding was completed (region III).
The fluctuations were obtained by
measuring the residual from linear fits to
the data (red dotted lines).
Fernandez and Li, Science 303, 1674 (2004)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 26
We show four different traces from ubiquitin chains for which
we observed seven unfolding events (recorded at 100 to 120
pN) before relaxing the force. Hence, the unfolded length of
all these recordings is comparable.
(A) In the first recording, the force was quenched to 50 pN
(downward arrow). An instantaneous elastic recoil was
observed. However, the ubiquitin chain fails to fold, as
evidenced by ist constant length at this force. Upon
restoration
of a high stretching force (120 pN, upward arrow),
the ubiquitin chain is observed to elastically extend
back to its fully unfolded length.
(B and C) Recordings similar to that shown in (A) (seven
initial unfolding events), in which the force was quenched
further down to 35 pN. In contrast to (A), the length of the
ubiquitin chain was observed to spontaneously contract to the
folded length. In (B), the folded ubiquitin chain was observed
to unfold partially at the low force, whereas in (C) it remains
folded until the high stretching force is restored (upward
arrow). Several unfolding events mark this last stage, bringing
the ubiquitin chain back to its unfolded length.
(D) A case in which the force was quenched even further
down to 23 pN. In this case, the folding collapse was
completed in much less time (inset), clearly showing that the
probability of observing a folding event as well as its duration
is strongly force dependent.
The duration of the folding collapse in force dependent
Fernandez and Li, Science 303, 1674 (2004)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 27
The duration of the spontaneous collapse of an
unfolded ubiquitin chain (t; Fig. 2A) depends on the
total contour length of the mechanically unfolded
polypeptide (A) and on the magnitude of the
stretching force during refolding (B).
(A) Three sets of recordings grouped by force range
and plotted against their contour length.
The solid lines are linear fits to each set of data.
To observe the force dependency we grouped the
data from (A) at the highest range of contour lengths
for which the effect of the force is most evident (150
to 200 nm). We observed that the duration of the
folding collapse is exponentially dependent on
the force (B).
Duration of folding collapse depends onprotein length and on magnitude of quence
Fernandez and Li, Science 303, 1674 (2004)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 28
Two recordings of protein length (nm) as a
function of time, showing the folding trajectory of
a single ubiquitin.
As before, stretching at a high force (100 pN) is
followed by a quench to a low force of 26 pN
that lasts 8 s, followed by restoration of the high
stretching force up to 100 pN (bottom trace).
In both cases, a single ubiquitin was observed to
unfold at 100 pN. After the quench, the proteins
undergo a spontaneous collapse into the folded
state. Upon restretching, the folded ubiquitin is
observed to elastically extend back to its folded
length at 100 pN and then to unfold (second
recording)
.
Discrete fluctuations of several nanometers can
be observed shortly before the final folding
contraction. The final contraction occurred much
faster than the previous stage; however, it had a
finite rate (insets).
Protein length as a function of time
Fernandez and Li, Science 303, 1674 (2004)
12. Lecture SS 20005
Optimization, Energy Landscapes, Protein Folding 29
Conclusions
AFM technique allows direct monitoring of the folding pathway of single proteins.
Ubiquitin folding occurs through a series of continuous stages that cannot be easily
represented by state diagrams.
By studying how the folding trajectories respond to a variety of physico-chemical
conditions, mutagenesis, and protein engineering, we may begin to identify the
physical phenomena underlying each stage in these folding trajectories.
Fernandez and Li, Science 303, 1674 (2004)