*E*). The double-label (donor+acceptor) specimen is excited with the donor wavelength, the acceptor emission provided the uncorrected FRET signal and the donor emission (the donor channel) represents the quenched donor (

*qD*), the basis for the

*E*calculation. Our results indicate this is not the most accurate determination of the quenched donor signal as it fails to consider the donor spectral bleedthrough (DSBT) signals in the

*qD*for the

*E*calculation, which our new model addresses, leading to a more accurate

*E*result. This refinement improves

*E*comparisons made with lifetime and spectral FRET imaging microscopy as shown here using several genetic (FRET standard) constructs, where cerulean and venus fluorescent proteins are tethered by different amino acid linkers.

## 1.

## Introduction

In Förster resonance energy transfer (FRET) microscopy, detection of the sensitized emission from the acceptor—the FRET signal—is obtained by exciting the specimen containing both the donor and acceptor with the donor excitation wavelength. Accurate quantification of FRET signals requires the removal of spectral bleedthrough (SBT) contaminations, which include the donor SBT (DSBT) resulting from the donor emission that is detected in the FRET channel, and the acceptor SBT (ASBT) caused by the direct excitation of the acceptor at the donor excitation wavelength. Algorithms have been developed for various microscopy techniques to identify and remove the SBT contaminations, allowing accurate measurements of the energy transfer efficiency
$\left(E\right)$
.^{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} In filter-based FRET microscopy, signals are measured in the donor and acceptor emission channels separated using bandpass filters. In contrast, spectral FRET microscopy uses a spectral detector to measure signals over a continuous emission spectrum. Comparing FRET measurements from cells expressing FRET-standard proteins obtained by filter-based or spectral methods suggested a source of error in the filter-based measurements. Our model, which includes the DSBT signals in the quenched donor
$\left(qD\right)$
for
$E$
calculation provides a more accurate measurement of
$E$
in filter-based FRET microscopy not previously considered in commonly used algorithms.^{1, 2, 3, 4, 5, 6, 7, 8} This source of error is not an issue in spectral FRET microscopy, since DSBT is included in the
$qD$
used for calculating
$E$
. The new model was tested with measurements from GHFT1 cells^{13} expressing several different genetic (FRET standard) constructs, including C5V, C17V, and C32V, where cerulean (C) and venus (V) are directly tethered by either a 5, 17, or 32 amino acid linker.^{14} Additionally, a CTV construct was used, where C and V are separated by a 229 amino acid linker encoding the tumor necrosis factor receptor-associated factor (TRAF) domain.^{9} The results are confirmed with both time-correlated single photon counting (TCSPC) and frequency-domain (FD) lifetime measurements.

## 2.

## Methods

In our theoretical model, for a donor (D)-acceptor (A) FRET system, the energy transfer efficiency $\left(E\right)$ is defined as the energy transfer rate $\left({k}_{T}\right)$ divided by the sum of all deactivation rates of the excited state of D $({k}_{T}+{k}_{D})$ , where ${k}_{D}$ is the sum of its deactivation rates other than FRET. At the D excitation wavelength, the decay profiles of the excited D [ ${D}_{D}\left(t\right)$ in Eq. 1] and the excited A [ ${A}_{D}\left(t\right)$ in Eq. 2] are presented, where ${k}_{A}$ is the sum of the rates for deactivation of the excited A, and ${D}_{0}$ and ${A}_{0}$ are the absorbed intensities of the D and A at $t=0$ , respectively.

## Eq. 1

$${D}_{D}\left(t\right)={D}_{0}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}[-({k}_{D}+{k}_{T})t],$$## Eq. 2

$${A}_{D}\left(t\right)={D}_{0}{k}_{T}\left\{\frac{\mathrm{exp}[-({k}_{D}+{k}_{T})t]-\mathrm{exp}(-{k}_{A}t)}{{k}_{A}-({k}_{D}+{k}_{T})}\right\}+{A}_{0}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}(-{k}_{A}t).$$## Eq. 3

$$I{B}_{DD}={D}_{0}[{k}_{Dr}\u2215({k}_{D}+{k}_{T})]=Q{Y}_{D}{D}_{0}[1-E],\phantom{\rule{1em}{0ex}}Q{Y}_{D}={k}_{Dr}\u2215{k}_{D},$$## Eq. 4

$$I{B}_{DA}={D}_{0}\left(\frac{{k}_{T}}{{k}_{D}+{k}_{T}}\right)\left(\frac{{k}_{Ar}}{{k}_{A}}\right)+{A}_{0}\left(\frac{{k}_{Ar}}{{k}_{A}}\right)=Q{Y}_{A}{D}_{0}E+Q{Y}_{A}{A}_{0},\phantom{\rule{1em}{0ex}}Q{Y}_{A}=\frac{{k}_{Ar}}{{k}_{A}}.$$In spectral microscopy imaging, the
$I{B}_{DD}$
in Eq. 3 and
$I{B}_{DA}$
in Eq. 4 can be directly measured using the combination of linear unmixing and ASBT correction to estimate
$E$
.^{9, 10, 11, 12} In our spectral FRET method known as sFRET,^{10} using the D
$\left(I{D}_{DS}\right)$
and A
$\left(I{A}_{AS}\right)$
reference spectra obtained from the respective single-label to unmix a double-label
$\lambda $
stack obtained under the donor excitation
$\left(I{B}_{DS}\right)$
produces
$I{B}_{DD}$
and
$I{B}_{DA}$
images. Thus,
$E$
can be calculated by Eq. 5, which is derived from Eqs. 3, 4

## Eq. 5

$$E=\frac{\mathrm{coef}\cdot \mathrm{FRET}}{\mathrm{coef}\cdot \mathrm{FRET}+qD},\phantom{\rule{1em}{0ex}}\mathrm{FRET}=I{B}_{DA}-\mathrm{ASBT},\phantom{\rule{1em}{0ex}}qD=I{B}_{DD},\phantom{\rule{1em}{0ex}}\mathrm{coef}=\left(\frac{s{s}_{D}}{s{s}_{A}}\right)\left(\frac{Q{Y}_{D}}{Q{Y}_{A}}\right),$$^{10}

In filter-based microscopy imaging, separate bandpass filters are usually used to measure the signals emitted close to D and A peak emission wavelengths. In our filter-based FRET method known as PFRET,^{7} at the D excitation wavelength, two images of the donor- and acceptor-labeled specimen are acquired
$-I{B}_{Dd}$
in the D emission channel and
$I{B}_{Da}$
in the A emission channel. In contrast to the
$I{B}_{DA}$
image in spectral FRET, the
$I{B}_{Da}$
image acquired using the filter-based method also contains the DSBT signals emitted from the donor, in addition to the FRET and ASBT signals emitted from the acceptor. The
$I{B}_{Dd}$
image is commonly used to measure the
$qD$
signals for the
$E$
calculation, as shown in Eq. 6.^{1, 2, 3, 4, 5, 6, 7, 8}

## Eq. 6

$$E=\frac{\mathrm{coef}\cdot \mathrm{FRET}}{\mathrm{coef}\cdot \mathrm{FRET}+qD},\phantom{\rule{1em}{0ex}}\mathrm{FRET}=I{B}_{Da}-\mathrm{ASBT}-\mathrm{DSBT},\phantom{\rule{1em}{0ex}}qD=I{B}_{Dd},$$^{7}The DSBT signals appearing in the $I{B}_{Da}$ image in filter-based FRET are included in the $qD$ (the $I{B}_{DD}$ image) for the spectral FRET $E$ calculation [Eq. 5], but is not in the $qD$ (the $I{B}_{Dd}$ image) for the filter-based FRET $E$ calculation [Eq. 6]. Significantly, DSBT is actually part of $qD$ , so adding DSBT back to the $I{B}_{Dd}$ image can provide a more accurate $E$ measurement when using a filter-based FRET method, as shown in Eq. 7.

## 3.

## Results and Discussions

The use of FRET-standard fusion proteins allowed direct comparison of the energy transfer efficiencies
$\left(E\right)$
measured in intensity- and lifetime-based FRET microscopy. The representative decays (TCSPC) and phasor plots^{15, 16} (FD) of the C-alone and FRET-standard constructs (Fig. 1
) clearly demonstrate a shorter lifetime from C to CTV to C32V to C17V to C5V. In both TCSPC and FD FLIM measurements, the
$E$
of a FRET-standard construct was estimated from the donor (C) lifetimes determined in the absence (
${\tau}_{D}$
as unquenched lifetime) and the presence (
${\tau}_{DA}$
as quenched lifetime) of the acceptor (V) based on
$1-({\tau}_{DA}\u2215{\tau}_{D})$
:^{17}
${\tau}_{DA}$
was measured from the cells labeled with CTV, C17V, C32V or C5V; and the corresponding
${\tau}_{D}$
was determined from the cells labeled with C (for CTV), C32A (for C32V), C17A (C17V), or C5A (for C5V), where A (amber) is a nonfluorescent form of Venus.^{14}

In Fig. 2 , we summarized the results of the analysis of cells expressing the same FRET standard fusion proteins by the four FRET microscopy methods—spectral confocal FRET, filter-based confocal FRET with the $E$ determined by Eq. 6 or 7 (see Sec. 2), TCSPC, and FD FLIM-FRET. For each construct, at least 12 cells were measured in each method and the $E$ at each pixel of each cell. The $E$ columns and inserted table represent the average $E$ of all analyzed pixels in all cells. The coef (0.635) value involved in the $E$ calculation in spectral or filter-based confocal FRET was determined empirically using the C5V $E$ obtained by the TCSPC FLIM-FRET method as a reference. Both the columns and the numbers in Fig. 2 clearly demonstrate that the theoretically derived Eq. 7 produces an $E$ for filter-based confocal microscopy that more closely matches the lifetime or spectral FRET measurements. Based on our PFRET results, the accuracy of $E$ increases by including the DSBT in $qD$ [Eq. 7]. The refinement of the $E$ calculation presented here is of particular interest to those researchers who use multiple FRET methods, sometimes simultaneously, to achieve their research goals.

## Acknowledgments

This work was supported by the University of Virginia and the National Center for Research Resources, NIH RR021202 (AP).