V12: Folding of Single Proteins

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!



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)



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.



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)



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)



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)



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



Limitation of previous study

Free diffusion experiments can only be used to examine states that are

substantially populated at equilibrium.



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.



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)



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)



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



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)



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)



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)



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)



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.




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.




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)



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




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)



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.




Verification


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).



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)



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).




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




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




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




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.


V12: Folding of Single Proteins

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