# Live-cell quantitative FRET imaging made simple by autocalibration in QuanTI-FRET

Julien Leblanc, Alain H Lombard, Adrien Saumureau, Sylvie Costrel, Jean

Revilloud, Alexis Coullomb, Aurélie Dupont

► To cite this version:

Julien Leblanc, Alain H Lombard, Adrien Saumureau, Sylvie Costrel, Jean Revilloud, et al. Live-cell quantitative FRET imaging made simple by autocalibration in QuanTI-FRET. 2025. hal-05411094

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Distributed under a Creative Commons Attribution 4.0 International License
Live-cell quantitative FRET imaging made simple by
autocalibration in QuanTI-FRET

Julien Leblanc¹, Alain H Lombard¹, Adrien Saumureau¹, Sylvie Costrel¹,
Jean Revilloud¹, Alexis Coullomb², Aurélie Dupont¹*

¹Laboratoire Interdisciplinaire de Physique (LIPhy), Université Grenoble Alpes, Centre
National de la Recherche Scientifique, Grenoble, F-38000, France.

²RESTORE Research center, Université de Toulouse, INSERM, CNRS, EFS, ENVT,
Toulouse, France.

*Corresponding author(s). E-mail(s): aurelie.dupont@univ-grenoble-alpes.fr;

Abstract

Genetically-encoded biosensors based on the Fluorescence Resonance Energy Transfer (FRET) between two fluorescent proteins have the power to measure biochemical activity in living cells with the spatio-temporal resolution given by optical microscopy. The generalization of their usage is limited by the difficulties in obtaining quantitative results independent of the instrumental system or the expression level. We recently developed Quantitative Three-Image FRET (QuanTI-FRET), a method for calibrating the system and obtaining absolute values of the FRET probabilities. The method proved to be efficient but required additional constructs for the calibration, thereby adding experimental steps. Here, we propose taking advantage of the constant and known stoichiometry of intramolecular FRET biosensors to directly calibrate the system using the dataset of interest, e.g., biosensor experiments. We demonstrate this idea by comparing the results of both standard calibration and autocalibration obtained on live-cell images of the FAK biosensor. This autocalibration is possible because of the strong robustness of the QuanTI-FRET calibration with respect to the quality of the calibration dataset. With this work, we simplify the experimental protocol to obtain quantitative FRET by autocalibration, and we make it accessible through a publicly available Python software and a napari plug-in.

**Keywords:** Förster Resonance Energy Transfer, FRET, fluorescence, live cell imaging, biosensors

# 1 Introduction

Fluorescence (or Förster) Resonance Energy Transfer (FRET) is the non-radiative transfer of energy between two fluorophores of overlapping spectra resulting in emission of fluorescence by the acceptor while exciting the donor fluorophore. This is a short-range transfer that can only occur when the two fluorophores are a few nanometers apart, which is the scale of molecules and

molecular dynamics[1]. In the early 2000s, this photophysical principle has been combined with fluorescent proteins to give rise to the development of genetically encoded biosensors that rapidly became a powerful microscopy tool to monitor molecular and signaling dynamics in living cells[2, 3]. The most common design relies on a molecular recognition element coupled with two fluorescent proteins expressed in the same amino-acid
sequence, named intramolecular FRET sensor[4]. Numerous research teams have focused their work on the design and optimization of FRET biosensors with the dual objective of optimizing fluorescent proteins and tailoring the affinity and response of the biochemical sensing sequence[5, 6]. This represents continuous effort, as each biosensor is unique and dedicated to a specific biological question[7–9]. On the microscopy side, the quantitative measurement of FRET efficiency in living cells with good temporal resolution has also been a challenge, and efforts in microscopy and analysis methods are still needed to support the progress of biosensor usage. As it is already difficult to ensure on the biological side the specificity and sensitivity of the biosensor as well as the control of biological biases, the microscopic image acquisition and analysis must be as simple as possible, free of bias, and not introduce too many additional experimental steps. This constitutes the main objective of this work: to make state-of-the-art quantitative FRET imaging as simple as possible on any fluorescent microscope.

Different experimental approaches exist for measuring FRET in living cells[10, 11], the two main approaches consist in monitoring the change in fluorescence intensity or in the donor fluorescence lifetime. Fluorescence Lifetime Imaging Microscopy (FLIM) requires the measurement of the fluorescence lifetime of the donor fluorophore in the range of nanoseconds, and hence a specific, sophisticated, and expensive hardware. It has been regarded as the most quantitative method, as after a proper calibration and careful analysis, the donor fluorescence lifetime is an absolute value which does not depend on the hardware. Lifetime imaging was also considered slow and to require expert knowledge for analysis. However, during the past few years, the acquisition frequency of FLIM images has been greatly improved[12, 13], also with commercially available hardware[14, 15], approaching a relevant timescale for live-cell signaling (~ 1 second). The Phasor FLIM approach[16, 17] to graphically analyze lifetime images has facilitated the non-expert analysis even if the calculations behind are not trivial. We can also note that obtaining a FLIM system, either by upgrading a confocal microscope or by buying a fully FLIM-confocal system, is still expensive but in the same range as state-of-the-art confocal microscopes.

FRET imaging based on fluorescence intensity appears more accessible and simpler to implement. The requirements are similar to those for conventional fluorescence imaging in terms of signal-to-noise ratio, fluorescence intensity, or microscope hardware. The method requires in principle a smaller amount of photons than FLIM and is therefore more appropriate for long live-cell experiments. Unlike the fluorescence lifetime, the fluorescence intensity depends on the fluorophore concentration. In addition, as the donor and acceptor fluorescence spectra partially overlap, spectral crosstalk exist between the donor and acceptor emission channels. Some other biases that directly affect the FRET phenomenon, like the sensitivity to the physicochemical environment (pH, crowding, etc.), are also present in FLIM. Various strategies have been developed to measure FRET changes[18] via fluorescence intensity, mainly acceptor photobleaching, spectral imaging, and ratiometric imaging[19], the latter being the most compatible with dynamic FRET imaging in living cells. Quantitative calculation of FRET from the ratio of fluorescence images requires rigorous calibration, control experiments, and appropriate image analysis[20]. It is now generally accepted that corrections for spectral crosstalk require the acquisition of three different signals, also called the 3-cube strategy in live-cell imaging[21, 22], followed by the subtraction of the relevant signals, a method named sensitized-emission FRET.

This is not sufficient to obtain quantitative FRET efficiencies that are independent of the instrumental setup and fluorophore concentrations and that can be compared from one team to another. To go further, one strategy has been to perform complex experimental protocols that include biosensor saturation at the end of acquisition to obtain complete inhibition and complete activation[7], giving two boundaries to normalize the data between 0 and 100%. The other strategy has been to keep the experimental protocol simple with the possibility of acquiring still images or sequences. Then, to correct for imaging biases, various normalization methods have been proposed[23–27]. Our previous work[28] and other publications[29, 30] finally obtained an equation for the FRET efficiency, directly based on photo-physical equations, defining two correction factors.
Similar equations and correction factors are standard for studying biomolecular structural dynamics in single-molecule FRET assays[31]. Once the correction parameters are calibrated, absolute FRET efficiency and stoichiometry, i.e. relative abundance donor:acceptor, can be obtained[28, 30]. The main contribution of the QuanTI-FRET method has been the single-step calibration of the two correction factors based on the fitting in a 3D space of the intensities from millions of pixels, thus fully taking advantage of the statistics of the imaged pixels and making this calibration method extremely robust[28].

QuanTI-FRET calibration does not require acceptor photobleaching, purified proteins, or known FRET samples, but, as some other related methods[23, 29, 30], the calibration step was done on tandem constructs, named FRET standards. The requirements are two FRET standards exhibiting different FRET efficiencies and a known stoichiometry, they must consist in the same FRET pair as the sample of interest. In practice, we noticed that it may be difficult to obtain such FRET standards, particularly the exchange of fluorescent proteins from the original sequence to the ones needed for the application. This represents a real bottleneck in terms of time and effort. Here, we show that it is possible to perform the calibration directly from the dataset of interest, for instance, live-cell biosensor images. The requirements are a constant and homogeneous stoichiometry, i.e. intramolecular FRET constructs, and a hypothesis on the stoichiometry value, 1 donor: 1 acceptor in the case of a simple intramolecular construct. We compare the performance of this autocalibration procedure, which does not require additional constructs, with the original based on FRET standards and observe only a systematic error of 3% in FRET efficiency. To make quantitative FRET measurement accessible to all laboratories, we implemented this analysis, as well as the original one, in a plug-in for the Napari free software, and the Python code is made publicly available.

## 2 Material and Methods

To obtain the FRET standards with different fluorescent proteins compared to the original ones from Steven Vogel's group[32], we ordered the fluorescent proteins DNA sequences (eCFP and

YPet) flanked with restriction sites from Genewiz and cloned them into the original plasmids: C5V (Addgene plasmid #26394) and C17V (Addgene plasmid #26395) were gifts from Steven Vogel. For experiments with donor-only expressing cells and acceptor-only expressing cells, we used mECFP, a gift from Benjamin Glick (Addgene plasmid #38772) and YPet, a gift from P. Daugherty & M. Davidson (Addgene plasmid #54637)[33]. As biosensors, we used the Lyn FAK biosensor (Addgene plasmid # 78299) and the KRas FAK biosensor (Addgene plasmid # 78301), gifts from Yingxiao Wang. These are sensors of the FAK kinase with two different cellular localizations in lipid rafts ("Lyn" target) and in plasma membrane outside of lipid rafts ("KRas" target)[34]. All plasmids were transfected into NIH/3T3 cells (ATCC) about 24 hours before observation.

Imaging was done with a widefield imaging system based on a Zeiss Axiovert200M inverted microscope body equipped with an image splitter (Gemini, Hamamatsu) coupled to two sCMOS cameras (ORCA Flash4.0, Hamamatsu). Excitation was done with a 16-channel LED illumination system (pE-4000, CoolLED). The hardware control and image acquisition were centralized and done with an Inscoper system. The microscope stage and objective were maintained at 37°C. The donor fluorophore was excited at 435nm, the acceptor at 500nm. The fluorescence emission was first separated from the excitation via a triple line beamsplitter set (445/514/594 from Chroma) in the microscope body. The fluorescence emission was further splitted with a beamsplitter at 509nm (Semrock). Hence, in two camera snapshots, the three images required for the analysis were obtained.

All image analysis calculations were coded in Python. Raw fluorescence images were pre-treated by substracting the dark count of the camera and flattened by dividing with a fluorescence image obtained from a uniform fluorescent sample (Chroma slide). Brightfield images of microscopic beads were used to compute the registration matrix used to transform the $I_{DD}$ image obtained from a different camera than the two other channels. To retrieve the background signal, a region of interest outside cells was manually drawn in every image and the average of the signal was kept in each channel as the background value. When needed, pixels from inside
cells were selected from an automated thresholding in Fiji. All calculations were done pixelwise. The original Python code has been reworked to be easily usable by everyone. It is available on a public repository at https://gricad-gitlab.univ-grenoble-alpes.fr/liphy/quanti-fret or directly as a napari plug-in for people less familiar with python programming.

## 3 The original QuanTI-FRET calibration

The QuanTI-FRET method proposes calibrating the instrument and the FRET pair to simply calculate absolute FRET probabilities from triplet of images acquired under the same conditions and with the same FRET pair (see Fig.1). All the photophysical and instrumental factors are included in this calibration, leaving the variability of the results to biological origins. The method requires the recording of the fluorescence intensity from three channels: $I_{DD}$ from the donor-emission channel associated to the donor-excitation path; $I_{DA}$ from the acceptor-emission channel associated to the donor-excitation path (a.k.a. FRET channel); and $I_{AA}$ from the acceptor-emission channel associated to the acceptor-excitation path. The latter image does not appear in the FRET probability equation (Fig.1) but is in the stoichiometry equation that is used for the calibration. This channel is required to uncouple stoichiometry, i.e. the relative abundance between donor and acceptor molecules, from the FRET effect. Even with intramolecular FRET constructs, the apparent stoichiometry can vary from one place to another in living cells, for instance, because of differential maturation or degradation of the fluorophores. As in every quantitative fluorescence analysis, the QuanTI-FRET method requires careful image preprocessing to subtract the background, flatten the field, and register the image triplets. Several tools are available in different environments, we can cite FRET-IBRA in Python[35] and BaSiC in Fiji/ImageJ[36], among others.

Then, the first calibration step is common to other FRET quantification methods, and it consists of calculating the spectral crosstalk. For energy transfer to be possible, the emission spectrum of the donor fluorophore must overlap with

the acceptor excitation spectrum. Most of FRET-based biosensors are designed with genetically-encoded fluorescent proteins which have broad emission and excitation spectra. Hence, spectral crosstalk, in particular the bleedthrough of the donor fluorescence in the acceptor detection channel, is almost impossible to avoid in such applications. This effect can be strongly reduced by using Quantum Dots which have very narrow emission spectra and large Stokes shift[37, 38], but they may be more difficult to handle for live-cell imaging.

From donor-only samples, the ratio $\alpha^{BT}$ between the channels involved in the spectral bleedthrough, $I_{DA}$ and $I_{DD}$, is calculated pixel by pixel, giving as many values as pixels. To quantify the direct excitation of the acceptor fluorophore by the donor-excitation path, the ratio $\delta^{DE}$ between $I_{DA}$ and $I_{AA}$ is calculated. In both cases, this gives rise to additional, nonrelevant, photons in the FRET channel that have to be retrieved by corrections. The calculation of the crosstalk correction factors requires masks for every image to take into account only relevant pixels, e.g. pixels from fluorescent cells and not from empty areas around cells. A variety of segmentation tools have been developed over the past decade, from automatic threshold segmentation (embedded in Fiji / ImageJ, for example) to deep learning-based approaches requiring much more hardware time and energy (a zoo of AI models is available at https://BioImage.IO[39] in the framework of DeepImageJ[40]). A first quality check is good practice at this step. Both factors correcting the spectral crosstalk, $\alpha^{BT}$ and $\delta^{DE}$, have been obtained for each pixel. One can look at their dependency versus the fluorescence intensity per pixel, and possibly decide to discard pixels with a too low signal that deviate from the final result, which is taken as the median of all values.

After calibration of spectral crosstalk, two correction factors have yet to be determined: $\gamma^M$ corrects the relative detection efficiency in the two emission channels and $\beta^X$ corrects the relative excitation efficiency in the two excitation channels. They include both fluorophore properties and microscope settings:

$$ \gamma^M = \frac{\phi_A \eta_{Adet}^{Aem}}{\phi_D \eta_{Ddet}^{Dem}} \quad \text{and} \quad \beta^X = \frac{L_A \sigma_{Aex}^A}{L_D \sigma_{Dex}^D}. \quad (1) $$
<figure><img src="image_2.png" /><figcaption>**Fig. 1** Overview of the QuanTI-FRET pipeline. The method requires the acquisition of images in three channels and their classical pre-processing (background subtraction and pixel registration). The spectral crosstalk are then calculated from donor-only and acceptor-only images. The last calibration step is the fitting to a plane of all pixels represented in a 3D space, defined by the three imaging channels. This step requires a hypothesis about the stoichiometry donor:acceptor of the data and can be done on FRET standards[28] or directly on the construct of interest [this work]. After calibration, FRET probability maps (E) can directly be calculated.</figcaption></figure>

where $\Phi_i$ is the quantum yield of fluorophore i, $\eta_i^j$ is the detection efficiency of photons emitted by j in the channel i, $L_i$ is the excitation intensity at the wavelength chosen to excite i and $\sigma_i^j$ is the absorption cross-section of j at the wavelength excitation of i.

Compared to other similar methods[29, 30], the originality of the QuanTI-FRET method is to determine these two correction factors through the single-step fitting of all batched pixels. As samples are imaged in three channels, each physical point of a sample corresponds to three values. Hence, the data can be represented in the {$I_{DD}$, $I_{DA}^{corr}$, $I_{AA}$} 3D-space, each axis corresponding to an imaging channel (see Figure1). The data points obtained from the same experimental conditions and the same FRET pair do not spread randomly in this space. Indeed, the stoichiometry is given by:

$$S = \frac{I_{DA}^{corr} + \gamma^M I_{DD}}{I_{DA}^{corr} + \gamma^M I_{DD} + I_{AA}/\beta^X}, \quad (2)$$

as demonstrated in previous work[28]. This equation can be reshaped and interpreted as the equation of a plane:

$$\beta^X \gamma^M I_{DD} + \beta^X I_{DA}^{corr} = \frac{S}{1-S} I_{AA}, \quad (3)$$

where $I_{DD}$, resp. $I_{AA}$, is the fluorescence intensity in the [DD] channel, resp. in the [AA] channel.

$I_{DA}^{corr}$ is the fluorescence intensity in the FRET channel corrected for the spectral crosstalk as explained above. S is the stoichiometry in each pixel, $S = n_D/(n_D + n_A)$, where $n_D$ is the number of donor fluorophores in the pixel and $n_A$ the number of acceptor fluorophores. If all data points have the same stoichiometry, they all lie on the plane defined by equation (3) which includes the correction factors $\beta^X$ and $\gamma^M$. A given set of experimental conditions (laser power, filter set, fluorophores) including stoichiometry corresponds to one plane. To determine the equation of the plane i.e., $\beta^X$ and $\gamma^M$, Coulomb et al.[28] proposed using a set of FRET standards which are three constructs with a given stoichiometry (1 donor: 1 acceptor) and three different FRET probabilities. The FRET probability is given by:

$$E = \frac{I_{DA}^{corr}}{I_{DA}^{corr} + \gamma^M I_{DD}}. \quad (4)$$

All pixels with the same FRET probability should therefore lie on a single line, which must be included in the aforementioned 3D plane. The 3D plot in Figure1 shows the experimental points corresponding to the three FRET standards used by Coulomb et al.[28]. Three clouds along three distinct lines are visible; they correspond to the three FRET probabilities of the three FRET standards with the experimental variability.
The hypothesis of fixed stoichiometry was formulated on the calibration sample and was released when measuring samples of interest. The original work shows that the QuanTI-FRET calibration allows obtaining absolute values of the FRET probability directly comparable between labs, whatever the instrument or the settings used. In addition, for samples with constant stoichiometry, the cellwise stoichiometry was also obtained quantitatively. However, the stoichiometry can locally deviate from the expected one. This can be related to a locally low pH or the degradation of one of the two fluorophores. Hence, the deviation from the average stoichiometry may be used as a quality index on the calculated FRET probability, which is not accurate any more when the stoichiometry deviates. As an additional feature, Coulomb et al. designed a spatial quality filter in which the deviation from the expected stoichiometry defines a confidence index which is inserted as a weight into a Gaussian spatial filter (see [28] for further details). Overall, the performance of the original QuantI-FRET method was evaluated and compared with other similar works showing that the pixelwise analysis and the single-step determination of the two correction factors give excellent robustness with data of various quality.

# 4 Autocalibration directly from the biosensor images

Although very powerful and robust, a major difficulty appeared in the practical implementation of QuanTI-FRET on various FRET biosensors. The preparation of FRET standards with the same fluorophore pair as the sample of interest can be particularly tedious. Indeed, because fluorescent proteins have very similar sequences, some usual tools of molecular biology may lead to errors due to unwanted recombination events. This very first step appeared to require non-negligible efforts. In addition, once the FRET standards were obtained with the correct fluorophore pair, sets of images with cells expressing at least two different FRET standards (i.e. different FRET values) must be acquired under the same experimental conditions as the images of interest. It is not necessary to acquire this FRET-standard data set before doing the experiments of interest. Nevertheless, these are additional experiments and efforts that may

<figure><img src="image_3.png" /><figcaption>**Fig. 2** Comparison of the two calibration methods. A. Scattered plot of the experimental points from the FRET standards (blue square) and of the biosensors (orange circle). The planes were obtained by fitting the FRET standards (blue) or the biosensor dataset (autocalibration, orange) to the stoichiometry equation 3. B. Results of the FRET calculation on the biosensor dataset using the correction parameters obtained with the two calibration methods. The difference between the average FRET values is only 3%. C. Example of a cell expressing the KRas FAK biosensor, with the three fluorescence channels and the FRET maps obtained with the two calibration methods, they are shown after stoichiometry-deviation filtering.</figcaption></figure>

limit the use of the QuanTI-FRET method and the obtaining of quantitative FRET values.

As most of the current FRET-based biosensors consist of a unique amino-acid sequence encoding both fluorescent proteins and the actual sensing part, their stoichiometry can be considered constant and close to 1 donor for 1 acceptor. The experimental objective is thus to measure variations of the FRET efficiency, and not variations of the stoichiometry. The QuanTI-FRET calibration obtained by fitting the dataset to a plane in a 3D space requires a known stoichiometry. Hence, if we consider the stoichiometry to be a known constant parameter in the case of biosensors, then the calibration can be performed on the data of interest. This holds true for any sample where such hypothesis on the stoichiometry can be
made. Of course, after calibration, the calculated stoichiometry on every pixel is not an independent measurement anymore but a deviation to the hypothesized stoichiometry used for calibration. An important requirement for the autocalibration to be valid concerns the FRET values distribution. As mentioned earlier, all points that represent the exact same FRET probability are located along a single line in the 3D space {$I_{DD}, I_{DA}^{corr}, I_{AA}$}. Hence, the fitting of a plane requires at least two FRET values, or spread FRET values; the more spread, the better. So the dataset used for the calibration must represent different FRET values. This can be naturally the case for biosensors reporting a variable signal in living cells or can be pushed by the used of specific drugs to activate on inhibit the targeted biological signal.

To verify that this idea is valid and gives relevant results, we acquired images of cells expressing the FAK biosensors[34] and images of cells expressing the corresponding FRET standards (see Materials and methods). As a preliminary step, images obtained from donor-only and acceptor-only expressing cells were used to calculate the spectral-crosstalk correction factors, $\alpha^{BT} = 0.673 \pm 0.002$ and $\delta^{DE} = 0.043 \pm 0.01$. Then, we conducted the analysis with the previously published QuanTI-FRET method, i.e. a first calibration step using FRET standards before the FRET calculation of the biosensor dataset. The FRET standards data points are shown in blue in Figure 2A, while the biosensor data points are shown in orange. The biosensor fluorescence signal appears very low compared to the FRET standards, about five times weaker. This situation is representative of most FRET biosensor experiments, where the expression level of the biosensor is crucial to not bias the biochemical signal to measure. On the one hand, the least-square fitting of the FRET standard dataset to a plane yielded $\beta^X = 4.02$ and $\gamma^M = 1.75$ with a coefficient of determination $R^2 = 0.983$. On the other hand, the least-square fitting of the biosensor dataset to the plane yielded $\beta^X = 4.33$ and $\gamma^M = 1.56$ with a determination coefficient $R^2 = 0.703$. As expected given the different signal intensities of the two datasets, the fitting gave slightly different results and a lower coefficient of determination in the case of the autocalibration. The two corresponding planes are shown in the 3D space in Figure 2A, the visible offset remains small.

Following calibration, we calculate the FRET probabilities for every pixel of the biosensor images with the two sets of calibration factors. The overall results are shown in the boxplot Figure 2B. A systematic bias is observed in the cellwise FRET probabilities in the case of autocalibration $< E_{auto} > = 51\% \pm 4\%$ (N=37 images, mean $\pm$ standard deviation), compared to standard calibration $< E_{std} > = 48\% \pm 4\%$ (N=37 images, mean $\pm$ standard deviation). This systematic error was expected and can be calculated from the equation used to calculate the FRET probability (equation 4). The deviation in E, $\delta E$, resulting from the deviation in $\gamma^M$, $\delta\gamma^M$, is directly estimated by:

$$|\delta E| = \frac{I_{DD}/I_{DA}^{corr}}{(1 + \gamma^M I_{DD}/I_{DA}^{corr})^2} |\delta\gamma^M|. \quad (5)$$

Here, we have $< I_{DD}/I_{DA}^{corr} > = 0.6$, $\gamma^M = 1.75$ and $|\delta\gamma^M| = 0.19$, resulting in a deviation $< |\delta E| > = 3\%$ that is exactly what was found experimentally. Looking at equation 5, and given that $\gamma^M$ and the fluorescence intensities are positive quantities, it appears that the error on the FRET probability, E, must be smaller than the one on $\gamma^M$. We can also note that this propagation of the error to E does not depend on $I_{AA}$ nor $\beta^X$. What is not visible in this calculation is the dependence on the signal intensities of the images, which directly influences the accuracy of the fitting. This is clearly understandable from the 3D plot shown in Figure 2A where the FRET standards points are spread over a wide range of intensities, while the biosensor data set is dimmer and concentrates close to the origin.

A first assessment of the quality of the image processing is to visually check that the data points plotted in 3D form a cloud passing through $\{0,0,0\}$ and spreading about the fitted plane. An additional assessment of the quality of the calibration is to verify that the calculated FRET probability does not correlate, pixelwise, with the calculated stoichiometry nor with the fluorophore's expression level. To do so, the Spearman's rank correlation coefficient was calculated between E and S, resulting in $\rho = 8 \cdot 10^{-3}$ for standard calibration and $\rho = 3 \cdot 10^{-2}$ for autocalibration. Even if the Spearman's coefficient is lower in the case of standard calibration, in both cases $\rho \ll 1$
<figure><img src="image_4.png" /><figcaption>**Fig. 3** Simulation of QuanTI-FRET calibration based on dataset with various spread in *E*, *ΔE*, and *S*, *ΔS*. The color scale codes for the final error on the determination of *E* after calibration, |*E* − *E*<sub>th</sub>|. The average error for each *ΔE* is plotted on the upper subplot. The final error on *E* depends strongly on *ΔE* and barely on *ΔS* with a relative error on *E* smaller than 10% for *ΔE* ≥ 0.17. This cutoff varies with the fluorescence intensities, in this example the average intensities are *I*<sub>DD</sub> = 48, *I*<sub>DA</sub> = 56, *I*<sub>AA</sub> = 85, see supplementary materials for details.</figcaption></figure>

showing that there is no clear monotonic relation-
ship between FRET probability and stoichiome-
try. We also calculated the Spearman’s coefficients
between *E* and *I*<sub>AA</sub>, the only channel not affected
by FRET and just related to the fluorophore con-
centration. The resulting Spearman’s coefficient
was identical for both calibration methods, *ρ* =
2 · 10<sup>-1</sup> << 1. With respect to this criterion and
with this dataset, the autocalibration performs as
well as the standard calibration.

To further investigate the robustness of the
QuanTI-FRET autocalibration method, we per-
formed simulations varying the spread in S and
E of the input data. We simulated the fluores-
cence intensities I<sub>DD</sub> and I<sub>DA</sub> based on esti-
mates of photophysical parameters, the number
of donor fluorophores, and specific values of E,
with a spread ΔE (see the supplementary mate-
rials for a detailed description). To calculate the
number of acceptor fluorophores and I<sub>AA</sub>, the
stoichiometry was taken from a uniform distribu-
tion of width ΔS. For each setting {ΔE; ΔS},
about 10<sup>6</sup> points were generated and used for the
QuanTI-FRET calibration, resulting in a pair of
parameters {γ<sup>M</sup>; β<sup>X</sup>}, which were compared to
their theoretical values. From that, the apparent

FRET *E* and the difference from the expected *E*<sub>th</sub> are calculated. We observe that the final error in the determination of the FRET probability, *E*, depends mainly on the spread *ΔE* in the calibration dataset and barely on the spread *ΔS* (Fig. 3). This is due to the error on *β*<sup>*X*</sup> being strongly correlated to *ΔS* while the error on *γ*<sup>*M*</sup> is strongly correlated to *ΔE*. It is important to note that the result of the 3D fitting also depends strongly on the fluorescence intensity; results of numerical simulations performed with three intensity levels are shown in supplementary materials. The case shown in figure 3 is relevant for common experimental conditions. For comparison, the experimental data shown in figure 2 had FRET values spread over 17% with rather low fluorescence intensities resulting in a final difference in *E* of only 3% compared to the calibration obtained from very bright FRET standards. In summary, the crucial points are the fluorescence signal and the spread in *E*, whereas a well-defined stoichiometry is not critical.

Even if a global hypothesis on the stoichiometry of the dataset used for the calibration was made, the apparent relative stoichiometry can be calculated on every pixel and may vary. Indeed, the hypothesis on the stoichiometry is done on the plane equation used to fit the whole dataset at once. Only pixels lying on the plane will show the apparent stoichiometry as forced in the fit equation. As mentioned above, a spatial quality filter based on the stoichiometry deviation can be used to refine the calculated FRET maps. Figure 2C shows an exemplary cell expressing the KRas FAK biosensor (see Material and Methods section). The three fluorescence channels, I<sub>DD</sub>, I<sub>DA</sub>, and I<sub>AA</sub>, show the apparent quality of the images with a particularly low signal in the donor channel. The filtered FRET maps resulting from the calculation with the two calibration methods are shown on the right. The background is filtered out by the spatial quality filter. As expected, the small systematic deviation is homogeneous throughout the cell.

5 Discussion

As pointed out by Smith et al.[41], the main
limitation of the sensitized-emission method com-
pared to the fluorescence lifetime method is the
number of measurements needed to obtain the
quantitative FRET analysis. Most of which are
used for calibration. The calibration of spectral
crosstalk, with donor-only and acceptor-only sam-
ples, remains essential. Only the correction for
direct excitation of the acceptor, δ<sup>DE</sup>, may need
to be calibrated again if the excitation intensities
are varied in different experiments. The correction
for the spectral bleedthrough, α<sup>BT</sup>, only depends
on the fluorophores and the hardware. Most of the
quantitative methods to measure FRET from the
sensitized-emission rely on additional samples or
experiments, known-FRET samples, FRET stan-
dards or photobleaching experiments [23, 26, 30,
42]. Jiang et al. proposed an optimization proce-
dure to determine the calibration parameters with
initial values based on photophysical data [43].
Here, we propose applying the necessary stoi-
chiometry hypothesis directly on the data set of
interest, thereby relaxing the need for additional
experiments on FRET standards and the efforts
in molecular biology needed for their production.
Often in live-cell FRET-biosensor experiments,
a relatively low expression level is required to
avoid influencing the biological signal to mea-
sure. Here, we used a biosensor dataset with quite
low fluorescence signals, especially from the donor
fluorophore (eCFP). Hence, we show that the
method is valid and robust to low-signal datasets
and can therefore actually be a good strategy for
real biosensor experiments. Because the QuanTI-
FRET protocol is extremely robust to the quality
and size of the dataset, due to the single-step fit-
ting of millions of pixels, we show that it can
efficiently be used to bypass the FRET stan-
dard calibration and directly calibrate on the
images of interest. As the calibration accuracy
of QuanTI-FRET relies in part on the broadness
of the FRET distribution, it may be helpful to
use biosensor samples after addition of activating
or inhibiting drugs. As for all sensitized-emission
quantitative methods, the calibration is valid for
given experimental settings. However, by making
the calibration easier and directly on the data
set of interest, it is now possible to repeat the
calibration when needed.

In general, FRET measurements have been
developed and pushed to their limits in single-
molecule assays. In recent years, the single-
molecule FRET community has done tremendous
work to unify and standardize their protocols and

analyses methods [44] as well as to assess the
uncertainty of single-molecule FRET experiments
[45] to address complex and dynamic structural
biology questions. This collective effort is still lack-
ing in the field of live-cell FRET imaging. How-
ever, impressive progress and efforts have been
made in the continuous development and improve-
ment of FRET sensors to broaden applications
in biology: toward biomolecular dynamics with
the characterization of protein-protein interac-
tions in living cells [46, 47] and toward functional
in vivo imaging with continuous optimization of
sensors[41, 48]. For these complex applications,
the ability to calculate absolute FRET values
directly from images would be valuable to avoid
further complicating the imaging and biolog-
cal protocols. Hence, there is no need to com-
pare an initial time to normalize the observed
effect[48] or to damage the sample by acceptor
photobleaching[41]. The autocalibration strategy
allows to work on independent batches of images,
and apart from the crosstalk calibration which
is in any case a requisite, the calibration is not
a limit anymore. The QuanTI-FRET autocali-
bration facilitates high-throughput protocols and
quantitative comparison between various condi-
tions or laboratories.

Conclusion

The general use of sensitized-emission FRET
methods for quantifying FRET in live-cell exper-
iments suffers from the additional experimental
steps for calibration, which are necessary to obtain
unbiased FRET probabilities. If the calibration
of spectral crosstalk remains essential, we show
that the two remaining correction factors can be
directly calibrated on the images of interest, for
instance, the biosensor dataset. The only require-
ment is the hypothesis that the donor:acceptor
stoichiometry must be constant on average, which
is the case for intramolecular FRET biosensors.
However, our simulations suggest that the spread
in *S* is not critical, which may make autocalibra-
tion possible on intermolecular constructs. Using
biosensor images may result in a low fluorescence
signal compared to FRET standard images, but
we demonstrated with experiments and simula-
tions, that the calibration quality remains excel-
lent, in typical live-cell imaging conditions, due
to the global fitting that gives the QuanTI-FRET
approach exceptional robustness. The method also benefits from an inherent confidence index in every pixel, given by the deviation from the expected stoichiometry. We make the code available on a public repository as a stand-alone and as a Napari plug-in for a graphical version. We believe that the autocalibration of the QuanTI-FRET method will reduce the complexity of quantitative FRET imaging thereby enabling the use of common fluorescence microscopes to confidently measure quantitative FRET biosensors in living cells and small animals.

**Acknowledgements.** The authors thank Irène Wang for her indirect contribution through continuous help and scientific discussions. A.D. is part of the GDR AQV and of the federation OLIMPICS. The authors have applied a CC-BY public copyright license to the present document and will be applied to all subsequent versions up to the Author Accepted Manuscript arising from this submission, in accordance with the grant's open access conditions.

**Funding.** Financial support was received from Linksium (N°CM190014) and from the Agence Nationale de la Recherche (ANR-21-CE18-0060-02).

**Competing interests.** The authors have no competing interests to declare relevant to the content of this article.

**Code availability.** Both modalities of the QuanTI-FRET method are available as a standalone Python code and as a napari plug-in from https://gricad-gitlab.univ-grenoble-alpes.fr/liphy/quanti-fret and from the Napari website https://napari-hub.org/plugins/quanti-fret.html.

**Author contribution.** AD obtained funding, conceived the project, contributed to the code, analyzed the data and wrote the first draft of the manuscript. JL performed cell biology and live-cell microscopy experiments. AHL performed live-cell experiments and contributed to the analysis. AS rewrote the code to create the final software. SC performed experiments and maintained the microscope. JR designed and performed the molecular biology part. AC contributed to the design of the method and to the first version of the Python code. All authors reviewed the manuscript.

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