Fluorescence Resonance
Energy Transfer
(FRET)
FRET theory
FRET theory
Excitation and emission spectra are separated by the Stokes shift
This process is represented in a Jablonski diagram
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Absorption ≠ excitation, though they’re often conflated.
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FRET theory
If the two fluorophores are physically close together, the donor can transfer its energy to the
acceptor, which radiates according to its emission spectrum.
This requires
matching of excitation / emission spectra
close physical proximity.
alignment of dipole moments
The FRET efficiency (fraction of energy transferred) is EFRET =
index of refraction
quantum efficiency
where the Forster radius R0 is
!
R0 (Å) ≡ 8.79 × 10
and the spectral overlap integral is
J(M
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In practice it’s best just to look up R0 for the particular donor/transfer pair of interest.
Typically, R0 is between 20 to 100 Å.
FRET theory
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Roy et al, “A practical guide to single-molecule FRET”
Nature Methods 5:507-516 (2008)
Lori Goldner
FRET data
FRET data
138
P. Kumar et al. / Analytica Chimica Acta 536 (2005) 135–143
Kumar et al., Analytica
Chimica Acta 536:
135–143 (2005)
FRET produces spectra like:
In principle you could take an entire spectrum and
fit to fobs (λ) = rfD (λ) + (1 − r)fA (λ)
Fig. 1. Raw FRET data recorded at three pH values (5.30, 5.60 and 6.10) and five ionic strengths (0, 20, 50, 70 and 100 mM NaCl).
In practice you usually only know the integrated spectrum in some window given by the
emission filter(s)
fer [8]. Experimental FRET data show baseline drift and different average intensity among experiments, which are due
to several factors related to the instrumental variability often
found in fluorescence studies. In this case, the effect of these
factors is still more dramatic because the data were recorded
in independent experiments over the course of several weeks.
In order to eliminate these systematic variations unrelated to
concentration of the different conformations, FRET spectra
were preprocessed by means of the normalization procedure
described above.
the results of the application of MCR to the data of melting
experiment carried out at pH 6.10 and 100 mM ionic strength.
When two components were considered, chemically meaningful concentration and spectral profiles were resolved. In
this case, the resolved initial and final components can be
easily related to ordered and disordered DNA structures, respectively. However, relatively large residual errors showing
a systematic variation during the melting experiment were
obtained. The magnitude and shape of these residuals could
be related to instrumental or experimental sources, or to the
presence of a third DNA structure. Therefore, a new analysis
was carried out, now considering three components. In this
case, the residuals are significantly lower and their shape is
closer to random noise. However, residuals still show a certain systematic variation at lower temperature values, which
could reflect a lack of fit in this region for this model. In this
case, the initial and final components can be related to the
ordered and disordered DNA structures, respectively. However, finding a biophysical explanation for the intermediate
component is rather difficult.
Classical univariate analysis of FRET data is based on the
assumption of monophasic transitions, i.e. on the presence
of only two conformations. For more complicated systems,
determination of Tm values from univariate analysis is rather
difficult. Tm values determined from the MCR resolved con-
Typically use a high wavelength bin centered on acceptor (IA) and a lower wavelength band for direct donor
emission (ID).
3.1. Individual analysis
You almost always get some direct excitation of A
exact amount depends on the choice of excitation wavelength
First, an individual analysis by MCR of each data matrix
was carried out in order to compare these results with those
obtained from the classical analysis. The first step in MCR,
i.e. the determination of the number of components (N), was
rather difficult because of the high overlap of concentration
and/or spectral profiles. For those cases where N was difficult
to uncertain, analysis was carried out considering two, three
or even four components. In general, the resolution with only
two components gave resolution errors larger than expected.
On the contrary, resolution with three or four components
provided concentration and spectral profiles which were not
always chemically meaningful. As an example, Fig. 2 shows
Observed range of FRET efficiencies is usually mapped empirically to 0-100% populations
Typically 0.15 <
IA − ID
< 0.95
IA + ID
0<f <1
The normalized FRET efficiency f can be used is like any other measure of fractional activity, occupation, etc. for
equilibrium analysis
FRET data
Population averages vs single-molecule studies
Population-averaged FRET measures the average distance between two points
Much faster. Cannot distringuish between a bimodal distribution and an intermediate normal distribution
Single-molecule FRET reveals the distribution of distances and kinetics of transition
Very time consuming
Data might consist of timeresolved images in two
color channels:
Red and green signal from
each spot are digitized:
FRET data
2%6)%7
Acceptor bleach
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Nature Publishing Group http://www.nature.com/naturemethods
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Roy et al, “A practical guide to single-molecule
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Background
tions, which contribute the momentum for the directed molecular motions. One example is the class of enzymes called transFigure 7. Distributions of the intramolecular distance between the LID and the
CORE domain of E. coli adenylate kinase at equilibrium under folding condiferases, which catalyze the transfer of charged groups. Upon
tions determined by global analysis of the fluorescence decay of the probes atsubstrate binding, these molecules undergo structural changes
tached to residues 142 (on the LID domain) and 203 (on the CORE domain). A
to protect the active center from water to avoid abortive hyvery wide distribution was obtained for the apo-AK (c), an indication of the
drolysis[88, 89] and to catalyze the transfer reaction. The FRET exlack of well-defined structure of the molecule in solution. The mean and width
of the distribution was reduced by saturation with each one of the substrates
periments go beyond existing methods in studying the mechaseparately (a) for the AMP complex and (g) for the ATP complex. In the
nism of such dynamic molecular “nanomachines”.
presence of the two-substrates-mimicking inhibitor, AP5A, the distribution was
E. Coli adenylate kinase (AK)[90] catalyzes the transfer of a
shifted towards the closed form of the holo-AK and the width was drastically
phosphate group between adenosine triphosphate (ATP) and
reduced (b). Very fast rates of fluctuations of the distance between the two
labeled domains characterize the apo state (large intramolecular diffusion coefadenosine monophosphate (AMP). Both substrates bind at
ficient). The additional interactions contributed by the substrates essentially staopen clefts between the CORE domain and the two minor dobilized the closed conformations which were poorly populated in the apo form
adenylate
kinase
folding:
mains (LID and AMPbind) (Figure 6). The crystal structure
of theFolding
and thus
shifted the
Protein
Studied
bydistribution
FRET of the ensemble of conformations towards the
apo-AK shows that the transition to the enzyme substrates
closed conformations. This can be viewed as a folding transition.
FRET data
FRET in protein folding
folded
label
These results imply that, in the apo form, this phosphoryl
transferase can be viewed as only partially folded. Unlike the
fixed crystal environment, in solution the molecules exist as an
ensemble of multiple conformers, separated by small energy
barriers. Binding of each one of the substrates is associated
with substantial shift of the equilibrium interdomain distance
distributions towards the uniformly folded holo-AK structure
and a drastic reduction of the diffusion rates (0 !2ns"1 for the
holo-AK) as expected for the domain closure mechanism. Furthermore, even in the apo enzyme state, a sizable fraction of
the population ( # 10–20 %) is already in the closed conformation. This raises the possibility that the substrates bind to the
preformed active sites in a “select-fit” and not by “induced-fit”
mode. This approach was further extended in elegant studies
of flexible proteins and peptides using the frequency domain
denatured
intermediate
label
Figure 6. Ribbon diagram of the crystal structure of E. coli adenylate kinase
(AK) (PDB 1ake). The residues that were labeled are marked. (Generated with
the program MOLSCRIPT). The sites of attachment of the probes are marked.
Probably not the real distance
www.chemphyschem.org " 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
865
Figure 8. Sets of transient distributions of the distance between residues 169
Haas, “The Study of Protein Folding and Dynamics by Determination of Intramolecular Distance Distributions and
and 188 in AK in the denatured state (d), in the 5 ms refolding intermediate
Their Fluctuations Using Ensemble and Single-Molecule FRET Measurements” ChemPhysChem 6:858–870 (2005)
state (c) and in the native state [after 3 seconds, (a)]. The protein was
denatured in 1.8 m GndHCl for 100 seconds and then the denaturant was diluted to final concentration of 0.3 m. Repeated traces are shown to demonstrate
the range of experimental uncertainty in the parameters of the distributions.
(The scale of the dashed curve centered around 30 ! was reduced 10 times in
order to fit the normalized narrow distribution) This experiment shows that in
ChemPhysChem 2005, 6, 858 – 870
Figure 9. Nat
within the de
beled at the N
at residue 20
three domain
FRET data
chymotrypsin inhibitor 2 folding:
The labeled
analyzed by
383.2 ! 0.5
CI2], consish Cy5-onlysized in this
ental setup,
l elsewhere
on-ion laser
ominally 100
s separated
DRLP 530,
ng light was
nd dichroic
ass filter for
Cy5 channel
photodiodes
tely and siccasionally,
olecules difved. These
shold of 30
E, and the
e, the factor
or quantum
s previously
Gaussians to
(11). Inter[1]
3 Å for the
for %2, the
Fig. 1. CI2 structure, showing points of dye attachment and destabilizing
mutation.
Fig. 2. (a) sp-FRET histograms of pwt CI2 at 3, 4, and 6 M denaturant. (b)
sp-FRET histograms showing comparison of pwt and mutant CI2 (K17G) at 3.5
Deniz et al, “Single-molecule
protein
folding:
Diffusion
M denaturant. Solid
lines show
Gaussian
fits to the peaks.
distance information for pairs of points on the amino acid chain
fluorescence
resonance energy transfer studies of the denaturation
as a function of folding, i.e., it can provide
a reaction coordinate
that affords a global view of the conformational distributions and
of chymotrypsin inhibitor 2”, PNAS 97:5179-5184 (2000)
dynamics of the protein as it folds. Recently, single-molecule
CI2(1–64) with M40C and N-terminal TMR substitutions. We
FRET has been used to examine the folding and fluctuations of
refer to this amino acid sequence as pwt CI2. The second dye,
the surface immobilized peptide, GCN4 (17). It is clear that
surface interactions could have modified and broadened the
Cy5, was coupled to the unique cysteine at position 40, affording
distributions observed under these immobilized conditions,
site-specifically donor-acceptor labeled protein, with a minimum
making the interpretation of the results and comparison to
existing ensemble measurements more problematic. RNA foldof purification!separation steps. The product was characterized
ing and protein fluctuations under surface immobilized condiby using HPLC and mass spectral analysis.
tions, and DNA hairpin folding in diffusion also have been
recently reported (10, 16, 18). In this work, we use diffusion
with the ensemble
are found to be
observation derive
fluorescent or pho
ensemble numbers
they are shifted tow
values.
The histograms
CI2 folding transit
per molecule in th
diffusion process
integration time. T
cates that the inte
must occur on a ti
integration time. T
unfolding kinetics
region by ensembl
A mutant (pwt
significantly lower
molecule folding p
pwt. This helix des
shift the guanidini
denaturant (19). H
the observed frac
significantly reduc
sp-FRET histogra
folded form drops
the mutant. Becau
dramatic change m
FRET data
Single-Molecule RNA Folding Bokinsky and Zhuang
RNA folding
FIGURE 1. Reaction pathway of the hairpin ribozyme. (A) The two-way junction form of the ribozyme and a FRET labeling scheme. The Cy3
Bokinsky
Zhuang,
Folding”,
and Cy5 dyes serve as the fluorescent
donorand
and acceptor.
The “Single-Molecule
ribozyme was immobilizedRNA
to the surface
via a biotin-streptavidin interaction.
Tertiary interactions are indicatedAccounts
by the following
colors: red, g+1:C25
Watson-Crick
base pair;
green, ribose zipper; purple, U42 binding
of Chemical
Research
38:566-573
(2005)
pocket. (B) Following the structural dynamics and function of single ribozyme molecules. (Top and middle) A fluorescence time trace of a
single ribozyme that shows binding of a noncleavable substrate, docking, and undocking. Green and red lines are the fluorescence signals
from the donor and acceptor, respectively. The blue line is the FRET value, defined as the acceptor signal divided by the sum of the donor
and acceptor signals. The substrate-free ribozyme gives a FRET value at 0.4. Upon binding of a substrate the FRET value changes to 0.2,
indicating an undocked state. The FRET then exhibits stochastic transitions between two levels (0.2 and 0.8) that correspond to the undocked
–
+
‘waiting conformation’ of kinesin between steps remains contro~13 nm
13–16
α-Tubulin β-Tubulin
versial
—some models propose that kinesin adopts a one-head215
43
17–21
bound intermediate
, whereas others suggest that both the
kinesin heads are bound to adjacent tubulin subunits7,22,23.
Addressing this question has proved challenging, in part because
215–43
324–324
b
of a lack of tools to measure structural states of the kinesin dimer
400
(66)
(59)
400
as it moves along a microtubule. Here we develop two different
1 mM
200
AMP-PNP
single-molecule fluorescence resonance energy transfer (smFRET)
0
0
sensors to detect whether kinesin is bound to its microtubule track
600
400
(92)
(54)
by one or two heads. Our FRET results indicate that, while moving
400
200 nM ADP 200
ige1,2
in the presence of saturating ATP, kinesin spends most of its time
200
labeled
bound to the FRET
microtubule
withheterodymer
both heads. However, when nuc0
0
600
(71)
(85)
leotide binding becomes rate-limiting at low ATP concentrations,
400
10 mM Pi + 400
215–43
324–324
a
ein kinesin
that
waits for
ATP in a one-head-bound
state and makes brief
200 nM ADP 200
200
Trailing
Leading
3
215
ng ATP
transitions
to a two-head-bound
intermediate
as
it
walks
along
the
0
0
~3 nm
~8 nm
400
of microtubule.
proOn the basis of these results, we suggest
a model for
(63)
(43)
–1
200
the how
two transitions in the ATPase
50
U
ml
43
This particular kinesin is locked
cycle position324
the two kinesin
324 heads
200
apyrase
Both heads bound
mational
with
both head bound in 43-labeland drive –their hand-over-hand motion.
+
0
distinct FRET signals
ver, the
head leading conformation0
–0.2 0 0.2 0.4 0.6 0.8 1.0 1.2
–0.2 0 0.2 0.4 0.6 0.8 1.0 1.2
The
first
FRET
sensor
for
distinguishing
one-head-bound
from
–
+
depending on which is the
contro~13 nm
FRET efficiency
FRET efficiency
two-head-bound states is a kinesin
heterodimer
in
which
one
α-Tubulin
β-Tubulin
leading/trailing
head
e-head215
43
chain contains a single cysteine residue in the plusc
othpolypeptide
the
1.0
1.0
7,22,23
tip of the catalytic core (residue 215), and the other
.
its end-oriented
1 mM
10 nM
0.5
0.5
because
chain contains
a single
cysteine residue in the minus-end-oriented
AMP-PNP
ADP
215–43
324–324
b
0
0
n dimer
base of the400core (residue 43) (sensor
termed 215–43; Fig. 1a). (59)
The
(66)
400
ifferent
0
1
2
3
4
5
0
1
2
3
4
1
mM
second sensor
is a kinesin homodimer
in which a cysteine residue was
200
AMP-PNP
mFRET)
1.0
1.0
introduced in both chains at the beginning of the neck linker (residue
0
0
ule track
200
nM
10 mM Pi +
600 termed 324–324).(92)
324) (sensor
400
0.5
0.5
(54)
200 nM ADP
ADP
moving
400
To test our
FRET sensors, we first200examined
nM ADP 200 the FRET efficiency in
0
0
its time
200
a
kinesin
dimer
bound
statically
to
a
microtubule
with
the
non0
1
2
3
4
5
0
1
2
3
4
en nuc0
0
600 a nucleotide state in
hydrolysable
nucleotide
analogue
AMP-PNP,
(71)
(85)
Time (s)
Time (s)
rations,
400
10 mM P + 400
10,17,21,22
One head
bound
which both
kinesin
heads
are
bound
to
the
microtubule
.
kes brief
200 nM ADP 200
200
Figure 1 | SmFRET observations of head–head configuration of kinesin
FRET
signaldye)
doesn’t
change
longMaleimide-modified
the
Cy3 (donor dye) and Cy5
(acceptor
were
0
0
of the
under
a, Diagrams
much depending (43)
on which is various nucleotide conditions.
This particular
kinesin
hastwo-head-bound
215-label-head
400
odelreacted
for
(63)
with
the two cysteine residues
in these
FRET
constructs,
and
intermediate state of the kinesin dimer
on theAtmicrotubule.
Positions of
200
the
leading/trailing
head
bound.
2
s,
the
43-label-head
50
U
ml
n heads
200
single kinesin
molecules that contained
apyrase both Cy3 and Cy5 were
cysteine residues for dye labellingtransiently
are shownbinds
in red.
The neck
linker, neck
in leading
conformation
0
selected for0 smFRET observations with total-internal-reflection
coiled-coil and bound nucleotide are shown in green, blue and cyan
–0.2 0 0.2 0.4 0.6 0.8 1.0 1.2
0 0.2 0.4 0.612 0.8 1.0 1.2
nd from
respectively. b, Histograms of FRET efficiencies (from each frame of images)
fluorescence–0.2microscopy
. SmFRET efficiencies for the 215–43
FRET efficiency
FRET efficiency
ich one
of dye-labelled kinesin bound to the axonemes with 1 mM AMP-PNP (ATPsensor from
individual microtubule-bound heterodimers showed a
he plusc
like state),
200
nM ADP,
200 nM ADP/10
mM Pi or 50 U ml21 apyrase
1.0
1.0al, “How
bimodal distribution
of low (about
10%)
and high
(about
90%)
Mori et
kinesin
waits
between
steps”,
Nature
450:750-755
(2007)
he other
1 mM
10 nM
(nucleotide-free state). The numbers of molecules analysed are shown in
0.5
0.5
FRET efficiencies
(Fig. 1b), as expected
oriented
AMP-PNP if the two kinesin heads
ADPare
parentheses. Dotted lines illustrate peaks characteristic of putative two0
tubulin subunits 8 nm0 apart along a microtubule
1a). bound
The to adjacent
head-bound (red) and one-head-bound (green) states. The correlation of
0 (Fig.
1
2
3
4Supplementary
5
0 Figs
1
dueprotofilament
was
1a
and
12 and3 2).4 Our preFRET efficiencies with distance measurements is discussed in
FRET data
ween steps
Count
EFRET
EFRET
Count
Kinesin motion
i
EFRET
–1
FRET data
Molecular beacons
DNA or RNA hybridization probes with fluorophore / quencher pair
Synthesized with a specific loop sequence complementary to probe target
base-pairing zipper energy is chosen to be unfavorable compared to perfect hybridization but favorable compared
to a single nucleotide mismatch in target
Emission intensity increases upon binding
With two probes, color changes quantitatively depending on ratio of targets