Fluorescence Intensity FRET

If the acceptor is not directly excitable, the number of photons emitted per time by one (⁰) donor (^DF⁰) respectively one acceptor (^AF⁰) fluorophore is given by:

DF⁰ =φ(~r)^Dσ(1−E)^DQ

| {z }

Dσ^DAQ

AF⁰ =φ(~r)^Dσ E^DQ . (4.6)

φ(~r) is the spatial distribution of the photon flux density with amplitude φ₀ (Excitation Intensity Distribution, EID), considered to be constant in time. ^Dσ is the absorption cross section of the donor fluorophore at the excitation wavelength and E^DQ is the sensitized acceptor quantum yield due to FRET, while (1−E)^DQis the reduced donor quantum yield (^DAQ) due to the presence of a quenching acceptor. The energy transfer efficiency (see eq. 1.4, section 1.2) for this molecule can then be represented by the respective number of emitted photons:

E⁰ =

AF⁰

DF⁰+^AF⁰ . (4.7)

Thus the transfer efficiency can be calculated from the fluorescence count rate of the donor and acceptor fluorophore respectively.

The apparent FRET efficiency - spectral crosstalk

A typical FRET setup involves two detectors, one for detection of the donor emission and one for the detection of the acceptor emission. Since the fluorophores need to be spectroscopically close for the energy transfer to take place, donor fluorescence will not only be detected in the donor detection channel but also in the acceptor detection channel. Furthermore the acceptor, in practice, will also be directly excitable. The number of detected photons per time in the acceptor channel F^Atherefore has three different contributions:

F^A=^DF^A

| {z }

Lk

+^AF^A

| {z }

Dir

+^DAF^A

| {z }

F RET

. (4.8)

The upper left index indicates the fluorophore (D for donor, A for acceptor and DA for FRET mediated acceptor emission) whereas the upper right index denotes the detection

4.3. FRET Analysis 93

channel. Lk stands for donor fluorescence leaking into the acceptor detection channel and Dir stands for the direct excitation of the acceptor fluorophore, while F RET denotes the acceptor fluorescence due to the FRET process. Note that ^DF^A now denotes the photons detected in the acceptor channel emitted by a donor fluorophore whereas^DF⁰ in (4.7) is the number of photons emitted by a single donor fluorophore.

Usually, the first two contributions of (4.8) are non-zero and sources of systematic errors.

The donor detection channel, on the other hand, can be chosen to be unsusceptible to acceptor fluorescence:

F^D =^DF^D. (4.9)

Analog to (4.7) we now define the apparent FRET efficiency as the photon count rate of the acceptor detection channel divided by the photon count rate detected in both detection channels:

Eapp= F^A

F^D+F^A (4.10)

In contrast toE⁰as in equation 4.7,E_appis an experimentally accessible value. In the presence of spectral crosstalk the apparent FRET efficiency will always be higher than the expected FRET efficiency. This is illustrated in figure 4.6 showing the intensity FRET histogram for donor-only labeled P06. A FRET efficiency of zero would be expected since there is no acceptor fluorophore available. The measured FRET efficiency of about 0.2 is purely due to donor fluorescence leaking into the acceptor detection channel. This example underlines the necessity to quantify the amount of spectral crosstalk.

Let us now concentrate on the apparent FRET efficiency in more detail. The number of photons detected per time can be written as a function of excitation, emission and detection efficiency:

F =φ₀hniV ·σ·Q·g . (4.11)

φ₀ is the photon flux density of the excitation laser (the spatial average of the EID, introduced in section 2.4.1) which can be determined from the laser power measured behind the microscope objective,P₀ =φ₀hνA, whereA is the cross sectional area of the laser beam at the focus andhν the energy of the incident photon.

hniis the fluorophore number density and V is the confocal volume depending on excitation

94 4. Polyproline as Calibration Assay for FRET Distance Measurements

Fig. 4.6: Apparent FRET efficiency distribution of poly-L-proline labeled only with Alexa-555. Although this molecule has no acceptor fluorophore an apparent FRET efficiency of about 0.17 is measured due to spectral crosstalk.

as well as on the detection wavelength.

σis the absorption cross section which can be derived from the absorption coefficientα=σhni and g, the overall detection efficiency of the entire detection path of a specific detection channel. Since σ, Q and g are not directly observable we substitute their product with the molecular brightness σ Q g/hνA = β introduced in section 3.4. β includes molecular properties of the fluorophore as well as properties of the experimental setup e.g. the overall detection efficiency. Consequently β has to be indicated with two indices, the upper left for either donor or acceptor and the upper right for the detection channel.

The confocal volume V depends on excitation and detection but since only the detection wavelength is different for the two detection channels, we label the confocal volume of the donor detection channel with V^D and the confocal volume of the acceptor detection channel with V^A. We can now rewrite (4.8) and (4.9) as follows:

F^D =hν A φ_D n

V^D ·^Dβ^D(1−E) F^A=hν A φ_D

n

V^A·^Dβ^A(1−E)

| {z }

Lk

+hν A φ_A n

V^A·^Aβ^A

| {z }

Dir

+hν A φ_DA n

V^A·^DAβ^A·E

| {z }

F RET

. (4.12)

4.3. FRET Analysis 95

F is the number of detected fluorescence photons per time but for FRET analysis it is more convenient to count the fluorescence photons per burst. During a burst the number of particles hNi=hniV present in the confocal volume equals one if we are in the single molecule regime.

The number of photons detected per burst is given by the detected count rateF multiplied by the burst duration T. Instead of the detection volume now the burst duration depends on the detection wavelength and therefore on the detection channel and (4.12) becomes:

T^DF^D =hν A φ

T^D·^Dβ^D(1−E) T^AF^A=hν A φ

T^A·^Dβ^A(1−E)

| {z }

Lk

+hν A φ

T^A·^Aβ^A

| {z }

Dir

+hν A φ

T^A·^DAβ^A·E

| {z }

F RET

. (4.13)

With this equation we can calculate the apparent FRET efficiency:

Eapp= T^A_D

β^A(1−E) +^Aβ^A+^DAβ^AE

T^A[^Dβ^A(1−E) +^Aβ^A+^DAβ^AE] +T^D[^Dβ^D(1−E)]. (4.14) (4.14) gives the apparent FRET efficiency one would measure for a fluorescence burst caused by a FRET pair with energy transfer efficiencyE.

Without spectral leakage (^Dβ^A = 0) and without direct acceptor excitation (^Aβ^A = 0) we get:

E_app= F^A

F^A+F^D = E

E+ 1/γ(1−E), (4.15)

and therefore

E= F^A

F^A+γF^D . (4.16)

Withγ =T^{A DA}β^A/T^{D D}β^D being the ratio of the molecular brightness of acceptor and donor in its respective detection channels. This is the conventional formula used in most FRET publications, only valid if spectral crosstalk can be neglected. Figure 4.7 shows the influence of spectral crosstalk as well as different molecular brightness. While leakage and direct

96 4. Polyproline as Calibration Assay for FRET Distance Measurements

acceptor excitation mainly effects the FRET efficiencies for larger donor-acceptor separations (figure 4.7a), differences in molecular brightness of both fluorophores result in an apparent shifting of R₀ (figure 4.7b). Figure 4.7c shows the increasing deviation of the apparent from the FRET efficiency for increasing amounts of crosstalk and higher molecular brightness of the acceptor fluorophore.

FRET with Pulsed Interleaved Excitation (PIE)

Consider a sample consisting of FRET pairs, i.e. a donor and an appropriate acceptor fluorophore covalently bound to a molecular spacer at a suitable distance of a few nanometers to each other. These molecules are solved in a solvent at sub nanomolar concentration to allow for single molecule detection. Accurate determination of FRET efficiencies may be hampered in this situation by incomplete FRET molecules, namely those molecules which are missing the acceptor fluorophore (donor-only molecules) as well as those missing the donor fluorophore (acceptor-only molecules). Even if both fluorophores are present, it may also happen that one of them is photochemically or photophysically damaged and does not show fluorescence anymore, which means effectively that one of the chromophores is ”not present” as above. In FRET-imaging those ”broken” pairs can be identified by recording the image at donor excitation wavelength and then recording the same image again at acceptor excitation wavelength. In solutions, however, the average time a molecule needs to pass through the confocal region is in the order of milliseconds or below. Therefore the diffusing molecules have to be probed on a faster time scale with two laser pulses to make sure both measurements are done on the same molecule.

For this purpose pulsed interleaved excitation is applied, i.e. two picosecond laser pulses at different wavelengths are interleaved to excite alternately the acceptor and the donor at a repetition rate chosen that the pulse separation is longer than the fluorescence lifetime of the fluorophores but much shorter than its diffusion time. Time Correlated Single Photon Counting (TCSPC) is used for temporal analysis of the detected photons. Time gating of the detected fluorescence offers the possibility to distinguish between fluorescence excited by the first or the second laser.

Compared to a conventional FRET experiment, where donor and acceptor fluorescence is detected after donor excitation now three different fluorescence photon currents are detected:

4.3. FRET Analysis 97

1.0 0.8 0.6 0.4 0.2

apparent transfer efficiency

2.0 1.6

1.2 0.8

R/R₀

leakage 5% 10% direct 2.5% 7.5%

(a)

1.0 0.8 0.6 0.4 0.2

apparent transfer efficiency

2.0 1.6

1.2 0.8

R/R₀

acceptor brighter

1.5 x 2x

donor brighter

2 x 1.5x

(b)

1.0 0.8 0.6 0.4 apparent transfer effciency 0.2

1.0 0.8 0.6 0.4 0.2

transfer efficiency

acceptor brighter

2x 1.5x

leakage + direct 10%+7.5% 5%+2.5%

(c)

Fig. 4.7: The apparent FRET efficiency for (a) different amounts of spectral crosstalk (leakage and direct acceptor excitation), (b) different ratios of molecular brightness of donor and acceptor in their respective detection channels. (c) shows the increasing deviation of the apparent transfer efficiency from the transfer efficiency for variing amounts of crosstalk and different brightness of donor and acceptor fluorophore

98 4. Polyproline as Calibration Assay for FRET Distance Measurements

F_λ^D

D,F_λ^A

D and F_λ^A

A, where the upper index indicates the detection channel as before and the lower index stands for the excitation wavelength, e.g. F_λ^A

D are the photons detected in the acceptor detection channel following excitation with the donor excitation wavelength (λ_D).

The principle of a Pulsed Interleaved Excitation FRET (PIE-FRET) experiment is shown in figure 4.8a - 4.8c. Figure 4.8a shows an intact molecule with a high FRET efficiency, mainly emitting into the acceptor detection channel upon donor excitation (F_λ^A

D). In figure 4.8b on the other hand, the situation for a molecule with low FRET efficiency is shown, i.e.

upon donor excitation, fluorescence is mainly detected in the donor detection channel (F_λ^D

D).

Without the second laser pulse at λA this case would not be distinguishable from the case shown in figure 4.8c where the acceptor molecule is not present or does not fluoresce. Using PIE the acceptor fluorescence emission following excitation atλ_A(F_λ^A

A) can be evaluated and thus figure 4.8b and 4.8c can be distinguished. In the case shown in figure 4.8c no photons are detected upon excitation with λ_A in contrast to figure 4.8b which indicates the absence of a fluorescing acceptor.

The three detected photon currents have the following contributions:

F_λ^D

D =^DF_λ^D

D

F_λ^A_D =^DF_λ^A_D

| {z }

Lk

+^AF_λ^A_D

| {z }

Dir

+^DAF_λ^A_D

| {z }

F RET

F_λ^A_A =^AF_λ^A_A. (4.17)

Applying (4.11) and also substitutingσ Q g/hνA=β we get the number of detected photons per burst analog to (4.13) in the now three detection channels:

T_λ^D

DF_λ^D

D =hν_DA_λDφ_λD T_λ^D

D·^Dβ_λ^D

D(1−E) T_λ^A_DF_λ^A_D =hνDA_λDφ_λD

T_λ^A_D·^Dβ_λ^A_D(1−E)

| {z }

Lk

+hνDAλDφλD

T_λ^A_D·^Aβ_λ^A_D

| {z }

Dir

+hν A_λDφ_λD T_λ^A

D ·^DAβ_λ^A

D·E

| {z }

F RET

T_λ^A_AF_λ^A_A =hνAA_λAφ_λA

T_λ^A_A·^Aβ_λ^A_A

. (4.18)

Im Dokument Confocal Microscopy and Quantitative Single Molecule Techniques for Metrology in Molecular Medicine (Seite 106-113)