QuanTI-FRET: a framework for quantitative FRET measurements in living cells
Alexis Coullomb, Cecile M. Bidan, Chen Qian, Fabian Wehnekamp, Christiane Oddou, Corinne Albiges-Rizo, Don. C. Lamb, Aurelie Dupont
QQuanTI-FRET: a framework for quantitative FRETmeasurements in living cells
Alexis Coullomb , C ´ecile M. Bidan , Chen Qian , Fabian Wehnekamp , ChristianeOddou , Corinne Albig `es-Rizo , Don. C. Lamb , and Aur ´elie Dupont Univ. Grenoble Alpes, CNRS, LIPhy, Grenoble, F-38000, France Department of Chemistry, Center for Nano Science (CENS), Center for Integrated Protein Science (CIPSM) andNanosystems Initiative M ¨unchen (NIM), Ludwig Maximilians-Universit ¨at M ¨unchen, Germany Institute for Advanced Biosciences, Universit ´e Grenoble Alpes, INSERM U1209, UMR5309, F38700 La Tronche,France * [email protected] ABSTRACT
Förster Resonance Energy Transfer (FRET) allows for the visualization of nanometer-scale distances and distance changes.This sensitivity is regularly achieved in single-molecule experiments in vitro but is still challenging in biological materials. Despitemany efforts, quantitative FRET in living samples is either restricted to specific instruments or limited by the complexity of therequired analysis. With the recent development and expanding utilization of FRET-based biosensors, it becomes essential toallow biologists to produce quantitative results that can directly be compared. Here, we present a new calibration and analysismethod allowing for quantitative FRET imaging in living cells with a simple fluorescence microscope. Aside from the spectralcrosstalk corrections, two additional correction factors were defined from photophysical equations, describing the relativedifferences in excitation and detection efficiencies. The calibration is achieved in a single step, which renders the QuantitativeThree-Image FRET (QuanTI-FRET) method extremely robust. The only requirement is a sample of known stoichiometrydonor:acceptor, which is naturally the case for intramolecular FRET constructs. We show that QuanTI-FRET gives absoluteFRET values, independent of the instrument or the expression level. Through the calculation of the stoichiometry, we assessthe quality of the data thus making QuanTI-FRET usable confidently by non-specialists.
Introduction
The theory behind Förster Resonance Energy Transfer (FRET) was first successfully described in 1946 but its applicationto biological systems, particularly in living cells, has only become popular in the late 1990s with the cloning of fluorescentproteins. Since the first cloning of the Green Fluorescent Protein (GFP), fluorescence microscopy has rapidly become a standardtool in cell biology. Fluorescence labelling allows the localization of a protein of interest in space and time in a biologicalspecimen, from cells to animals. The labelling of several proteins in the same sample has been used to address protein-proteininteractions in terms of colocalization. However, using standard fluorescence microscopy, determination of protein-proteindistance is limited by the diffraction of light i.e., hundreds of nanometers. Förster Resonance Energy Transfer (FRET) methodscircumvent this barrier by allowing the detection of distances below 10 nanometers between a donor fluorophore and an acceptorthrough non-radiative energy transfer mediated by dipole-dipole interactions. FRET measurements can distinguish betweentwo proteins being in the same compartment or in direct contact. Moreover, the ability to measure nanometric variations allowsfor the detection of protein conformational changes . A large class of fluorescent biosensors have been engineered based onFRET to monitor protein function (kinase , GTPase ), calcium signals, or more recently, forces on the molecular scale .The most common design relies on a molecular recognition element coupled with two fluorescent proteins (FPs) expressed inthe same amino-acid sequence (intramolecular FRET sensor). An intermolecular FRET design is also possible where the FPsare inserted on two independent moieties. In this case, the apparent stoichiometry can strongly vary, which makes a quantitativeanalysis much more difficult.There are two main approaches for measuring FRET in living cells: one is based on the change in fluorescence intensity andthe other on the change in the donor fluorescence lifetime . Fluorescence LIfetime Microscopy (FLIM) requires sophisticatedinstrumentation and analysis, and is often recognized as a quantitative method for live-cell measurements. Different strategieshave been developed to measure FRET efficiency via the fluorescence intensity of the donor and/or of the acceptor, someinvolving the total photobleaching of one fluorophore or specific instruments for spectral imaging . The most compatiblemethod with dynamic quantitative FRET imaging and live-cell imaging is based on the sensitized-acceptor emission. Becausethe collected fluorescence intensity depends strongly on numerous instrumental factors (excitation, filter set, camera sensitivity a r X i v : . [ phy s i c s . b i o - ph ] D ec igure 1. A. A schematic of an experimental setup used for the validation of the framework is shown. Three images areacquired in two snapshots by automatically alternating the laser excitation and splitting the camera in two detection channelscorresponding the donor and acceptor channels. B. Framework for quantitative FRET analysis. The analysis requires threeimages combining the detection in the donor and the acceptor channels with the excitation of the donor and the acceptor. Acalibration step allows the determination of four factors correcting for the crosstalks and the relative excitation and detectionefficiencies of the donor and acceptor fluorophores. As a result, instrument-independent FRET probabilities andstoichiometries are calculated. Scale bar: 20 µ m.etc), this approach requires several corrections to calculate an instrument-independent FRET efficiency. The literature isrich of different correction factors and mathematical expressions of FRET indices . The idea of correcting for spectralcrosstalks and at least for the difference in detection efficiency between donor and acceptor channels emerged concomitantlyin the single-molecule and in the live-cell imaging fields . It is now generally accepted that bleedthrough of thedonor emission in the acceptor channel and direct excitation of the acceptor by donor excitation channel must be correctedby substracting their contributions. This requires the acquisition of three different signals, also called 3-cube strategy inlive-cell imaging . As such, the apparent FRET index varies with the fluorophore concentration and, even with additionalnormalization, the direct comparison of FRET values obtained independently is not possible . To account for photophysicalartifacts, we need to go back to physical equations and determine the origin of the signal in each channel. The next obstacle isthe experimental determination of the correction factors. Existing methods require samples with known FRET efficiency orknown concentration or even an additional experiment using acceptor photobleaching .In this work, we clarify the theory coming from single-molecule studies and adapt it to live-cell imaging. We presenta new method to determine all the correction factors in a robust manner without any additional photobleaching experimentor external calibration of the FRET efficiency. The only requirement for calibration is knowledge of the donor:acceptorstoichiometry, which is in general known by construction. The calibration can thus be achieved directly on the sample of interestor with FRET standards . While the stoichiometry can be accurately measured in the last case, this information can always beused as a quality factor to discard aberrant pixels. No specialized microscope is required as the QuanTi-FRET (QuantitativeThree-Image) method can be applied to any epifluorescence triplet of images acquired with commercial instruments. Here, wedemonstrate that QuanTI-FRET allows for absolute FRET measurements that are independent of the instrumental setup and ofthe fluorophore concentration. Being robust and including an inherent data quality check, the method can be used confidentlyby non-specialists, especially for FRET-based biosensors applications. Theory
To obtain as much information as possible from the sample, we follow a multiple excitation scheme (Fig. 1) as introduced byKapanidis and colleagues for single molecule spectroscopy and close to the three-cube method in live-cell imaging . Byswitching rapidly between both excitation sources, and splitting the emission into two channels on the camera, we acquire intwo successive snapshots four images: DD : the detected signal in the donor channel after excitation at the donor wavelength, I DA : the detected signal in the acceptor channel after excitation at the donor wavelength, I AA : the detected signal in the acceptor channel after excitation at the acceptor wavelength.The fourth image I AD contains no information, only noise, and is discarded. In principle, only I DD and I DA are sufficient tocalculate the transfer efficiency. That would be the case if the photons coming from the donor and the acceptor had the samedetection efficiency. In practice, it is not possible to have such an instrument and, several corrections must be considered toget unbiased quantitative FRET efficiencies. The third image, I AA , is independent from the FRET efficiency but is required tocalculate all the necessary corrections.One can write the intensity of the three types of signals as a function of the photophysical and instrumental parameters andthe population of the different fluorophores, n A (acceptor) and n D (donor), and FRET probability, E : I AA = n A L A σ AAex φ A η AemAdet (1) I DD = n D L D σ DDex ( − E ) φ D η DemDdet (2) I DA = n D L D σ DDex E φ A η AemAdet + n D L D σ DDex ( − E ) φ D η DemAdet + n A L D σ ADex φ A η AemAdet (3)where L i is the excitation intensity at the wavelength chosen for excitation of fluorophore i , σ ji is the absorption cross section of j at the excitation wavelength of i , φ i is the quantum yield of i and η ji is the detection efficiency of photons emitted by j in thedetection channel i . The expression of I AA is the simplest as it only depends on species A (acceptor). For I DD , one has to takeinto account the probability to transfer energy to the acceptor, E , as acceptor photons are not detected in this channel. Finally,to express I DA , the FRET image, not only the signal coming from FRET events must be taken into account but also the twocrosstalk terms: (i) the bleedthrough of photons emitted by the donor into the acceptor channel and (ii) the direct excitation ofacceptor molecules with the donor specific wavelength. Some of the parameters in the above equations are difficult to measure.We follow a pragmatical approach and avoid the systematic determination of all twelve unknowns. First, we can simplify theexpressions by defining a bleedthrough correction factor as α BT and a direct excitation correction factor as δ DE . Additionally, acorrection factor for the different detection efficiencies in both channels is defined as γ M , and similarly a correction factor forthe different excitation efficiencies in both channels is defined as β X α BT = η DemAdet η DemDdet δ DE = L D σ ADex L A σ AAex γ M = φ A η AemAdet φ D η DemDdet and β X = L A σ AAex L D σ DDex (4)Hence, the notation is simplified and by inverting the previous set of equations, we obtain the FRET probability: E = I DA − α BT I DD − δ DE I AA I DA − α BT I DD − δ DE I AA + γ M I DD (5)In addition, as in Lee et al. , we define the stoichiometry as the relative amount of donor molecules with respect to thetotal number of fluorophores in each pixel: S = n D n D + n A (6)From equations (1) and (2), we derive expressions for n D and n A and insert them into equation (6). By simplifying with theexcitation correction factor β X defined in equations (4), equation (6) reduces to: S = + I AA I DD β X γ M ( − E ) (7)To decouple stoichiometry and FRET probability, we replace E by the expression given in equation (5). Finally the stoichiometryreads: S = I DA − α BT I DD − δ DE I AA + γ M I DD I DA − α BT I DD − δ DE I AA + γ M I DD + I AA / β X (8) y including the crosstalk corrections into a corrected FRET image, I corrDA = I DA − α BT I DD − δ DE I AA , we obtain two masterequations defining the FRET probability and the stoichiometry in each pixel: E = I corrDA I corrDA + γ M I DD (9) S = I corrDA + γ M I DD I corrDA + γ M I DD + I AA / β X (10)Both E and S can be calculated from the three experimental images, I DD , I DA and I AA , and four parameters, α BT , δ DE , γ M and β X . All four correction factors are derived from the detailed expressions of the collected fluorescence intensities in the threedifferent channels. The notations were chosen according to the consensus in the single-molecule field with a supplementalexponent for a direct understanding of the role of each correction factor. The crosstalk correction factors are already widelyused in the 3-cube approaches and are straightforward to calibrate. Imaging a donor-only sample, in vitro or in cellulo,provides α BT ; similarly, imaging an acceptor-only sample provides δ DE . α BT depends only on the donor emission spectrum,the filter set and the spectral response of the camera. δ DE depends on the acceptor excitation spectrum but also on the ratio ofthe illumination power in the two channels. Under the same experimental conditions (same fluorophores, same filter set andillumination intensities), the crosstalk corrections to be brought to I DA depend only on the quantity of both fluorophores, givenby I DD and I AA while α BT and δ DE are unchanged.The two other correction factors, γ M ("M" for Emission) and β X ("X" for Excitation), are more difficult to determine. γ M accounts for the difference in the measured fluorescence emission when the same number of donor or acceptor molecules areexcited. Hence, it is related to the quantum yield and to the detection efficiency of the setup in each channel. β X accountsfor the difference in energy absorption for each channel. Hence, it is related to the illumination intensity and the absorptioncross-section of each fluorophore. γ M has already been described, in single molecule and in live-cell imaging . Severalindirect strategies have been developed to determine the value of γ M : from acceptor photobleaching , the use of a FRETsample with known FRET efficiency , an interpolation from two constructions with very different FRET values or a fit of therelation between 1 / S and E . β X has been introduced by Lee et al. for single molecule experiments and a similar parameterhas also been empirically introduced by Chen et al. for cells experiments . If β X and γ M are determined independently, β X has no effect on the FRET efficiency but just on the stoichiometry (see equations (9) and (10)) . Since the stoichiometry insingle molecule studies is often limited to donor only, acceptor only and donor:acceptor complexes, S does not need to beaccurate and β X is not necessary. On the contrary, we will show that S can be very useful in live-cell experiments even whenthe FRET construction has a well-defined stoichiometry. Calibration of the correction factors
Having described the theory directly from the physical parameters of the fluorophores and of the experimental setup, the difficultpart to achieve the calculation of quantitative FRET is to determine the four correction factors. As mentioned previously, thecrosstalk correction factors are measured from donor-only and acceptor-only cells, and calculated as the ratios α BT = I donor − onlyDA I donor − onlyDD and δ DE = I acceptor − onlyDA I acceptor − onlyAA (11)These ratios are calculated in each pixel of all the imaged cells and the median value is kept. The correction factors γ M and β X cannot be determined from the donor-only or acceptor-only samples where the FRET probability is equal to zero (or notdefined). Another piece of information is necessary and is found in the stoichiometry. Equation (10) can be rewritten as β X γ M I DD + β X I corrDA = S − S I AA , (12)which is the equation of a plane in the 3D space defined by { I DD , I corrDA , I AA }. If the stoichiometry is known, the strategy isto fit the experimental data { I DD , I corrDA , I AA } to a plane and thereby determine β X γ M and β X . If the FRET sample of interesthas an unknown stoichiometry, another calibration experiment has to be made with a defined stoichiometry FRET probe.Practically, the pixel values of a whole dataset (N cells) are gathered in vectors X = [ I DD , I corrDA ] and Y = [ I AA ] and the matrix A = [ γ M β X , β X ] is determined such as X . A = Y by a least-square fitting. If the sample shows only one FRET value E withdifferent fluorescence intensities (i.e. fluorophore concentrations), the pixel values will form a straight line in the 3D space{ I DD , I corrDA , I AA } (Fig.2). As a result, an infinite number of planes can fit the dataset. For a good determination of β X and γ M , itis therefore necessary that the FRET values of the dataset are sufficiently spread. The visualization and the calculation of thecorrection factors in the 3D space { I DD , I corrDA , I AA } is the originality of this work. We compare our approach with the two otherrelated methods in the last section. igure 2. FRET measurements on the three FRET standards, C5V, C17V and C32V. ( A ) Triplet fluorescence images areshown for exemplary cells transfected with the three FRET standards: C5V (short linker), C17V (medium linker) and C32V(long linker). The calculated FRET maps for the individual cells are shown on the right plotted using the same color scale. Thehighest FRET is observed for the shortest linker construct C5V and decreases to the lowest FRET construct C32V. Scale bar:20 µ m. Color bar: FRET efficiency in % ( B ) Scattered plot of all pixels values from all cells imaged in the { I DD , I corrDA , I AA }3D-space and the fitted plane, side view as inset. The three FRET standard populations forming three distinct clouds are alllying on the plane defined by β X and γ M . ( C ) Boxplot gathering cellwise FRET values of C5V, C17V and C32V measuredindependently in two different labs ([A] and [B]). After calibration, the same FRET median values were obtained. Results
Validation of QuanTI-FRET using FRET standards
To test the proposed method in live-cell experiments, we utilized the FRET standards developed by Thaler et al. and Koushiket al. . The FRET standards consist of a pair of fluoroscent proteins, a donor (Cerulean) and an acceptor (Venus), separatedby an amino-acid sequence of variable length. Three standards were used in the present work to calibrate the experimentalsetup: C5V, C17V and C32V, where the linker between donor and acceptor consisted of 5, 17 and 32 amino-acids respectively.The construct with the shortest linker, C5V, was expected to exhibit the largest FRET efficiency and the FRET efficiency todecrease as the linker length increases . The FRET standards were expressed in Hela cells and imaged on the setup describedin Figure1.As a first step for calibration, the crosstalk corrections corresponding to the donor, Cerulean, and the acceptor, Venus,must be determined. Hence, Cerulean-only cells and Venus-only cells were imaged. Using equation (11), the bleedthroughfor Cerulean was calculated as α BT = . ± .
002 (10 cells) and the direct excitation of Venus as δ DE = . ± . α BT and δ DE are shown in supplementary information (Fig.S1). The second stepconsists in the determination of γ M and β X , the factors correcting for the difference in detection and excitation efficiencies inthe different channels. The three necessary fluorescence images, I DD , I DA and I AA , of three exemplary cells transfected withC5V, C17V and C32V are shown in Figure 2A. All the pixel values { I DD , I DA , I AA } of all cells expressing the three constructswere gathered as one dataset and fitted with the plane equation (12) (Fig.2B). A mask of each cell was obtained and only thepixels coming from within the cells were kept. This equation has an additional unknown, S. An assumption on S is necessaryat this step. By design, the CxV constructs should have on average one donor for one acceptor, i.e. S = .
5. This assumesthe maturation efficiency of the donor and the acceptor are close to 1. We will discuss the influence of maturation in the nextsection. For S=0.5, the plane equation reduces to: β X γ M I DD + β X I corrDA = I AA . (13)A given set of experimental conditions (laser power, filter set, fluorophores, stoichiometry) corresponds to one plane, and in thisplane, a given FRET efficiency corresponds to a line. As seen in Fig.2B, the scattered data from the three standards appear aslinear clouds lying on the same plane defined by β X and γ M and the assumed stoichiometry S ( S = .
5, 1 donor:1 acceptor). ere, the least square fitting of the plane yielded β X = . ± .
008 and γ M = . ± .
02 with a coefficient of determination R = . S = .
5, the stoichiometry cannot be an output for this calibration dataset. Nevertheless, noassumption was made concerning E , and therefore, the FRET probability can be calculated on the same dataset as the one usedfor calibration. If the experiment of interest presents a sufficiently broad distribution of FRET probabilities to determine theplane in 3D, there is no need for a different experiment with FRET standards for calibration. Hence, calibration can be achievedon-the-fly on samples with known stoichiometry.More than 25 Hela cells expressing one CxV construct were measured. The median FRET probability was E C V = . s . d . = .
2, 26 cells) for C5V, E C V = . s . d . = .
8, 25 cells) for C17V and E C V = . s . d . = .
5, 27 cells) forC32V, calculated over more than 3 · pixels. The uncertainty comes rather from the cell to cell variability than from thepixel statistics. Hence, the median FRET value per cell was taken (Fig.2C, dataset [A]) and the uncertainty calculated asthe standard error of the mean yielding: E C V = . ± . E C V = . ± . E C V = . ± .
8. To verify that theFRET probability was independent of the fluorescence intensity, the Spearman’s rank correlation coefficient was calculatedbetween E and I AA , the only channel not affected by FRET and just related to the fluorophore concentration. Gathering the datafrom all three standards, the resulting Spearman’s coefficient was ρ = .
04, confirming the absence of correlation between thefluorescence level and the calculated FRET probability. This is also true pixelwise on a single cell basis (see SupplementaryFig.S2) and cellwise comparing all cells expressing one FRET standard (see Supplementary Fig.S3). Similarly, we questionedthe effect of the correction factor γ M by calculating the Spearman’s coefficient between E and the total donor fluorescence( γ M I DD + I corrDA ) without the correction, ρ = .
111 ( γ M = ρ = .
045 ( γ M = . i.e. ,obtained independently in different laboratories in the world. To test this, we performed the same experiments a second time ina completely independent way: with a different instrument, in a different country, by a different team on another cell culturewith fresh constructs ordered directly from Addgene. The experimental data was analyzed with the exact same procedure. Thecalibration gave the following correction factors α BT = . ± .
001 (12 cells) and δ DE = . ± .
003 (12 cells) for thecrosstalks and β X = . ± .
07 and γ M = . ± .
07 ( R = .
82) for the excitation and emission corrections. The FRETprobability was measured for the three FRET standards giving E C V = ± . E C V = ± . E C V = ± . R = .
82) of the 3D fitting and the standard deviation of the FRET probabilityfor each construct. Nevertheless, the FRET values obtained were in agreement with the first dataset ([A]). Hence, we showthat measuring FRET with the QuanTI-FRET method is quantitative: the absolute FRET values are meaningful and can becompared from one lab to another.
Taking advantage of S
So far, the stoichiometry was used only to calibrate the system. However, once the experimental system has been calibrated,the QuanTI-FRET analysis can determine both E and S independently. In this case, additional information can be extractedfrom S. First of all, S can be used to evaluate the quality of the calibration and of the dataset. As in single molecule studies,the 2D histogram combining the stoichiometry and FRET probability histograms (Fig.3A) is a useful tool . In theory, thestandard constructs with 1 donor for 1 acceptor should appear as a cloud corresponding to their average FRET efficiency, E ,and S = .
5. A known stoichiometry of 1:1 donor:acceptor is also reasonable for a biosensor construct that contains both donorand acceptor fluorescent proteins that fold and mature with high efficiency. However, when looking for interactions betweendifferent proteins, a fraction of donor only and/or acceptor only constructs are expected. If free acceptors are also present in theimage, the apparent FRET probability stays constant but the stoichiometry drops (Fig.3A). On the contrary, if free donor ispresent with the 1:1 construct, both S and E are affected. This variation can be described theoretically. If a solution containinga donor-acceptor construct, n D , with an average FRET efficiency of E is mixed with free donor, n f reeD , the apparent FRETprobability and the apparent stoichiometry are (see Supplementary Information): E app = + − E + n Df ree / n D E and S app = + n Df ree / n D / S + n Df ree / n D (14) igure 3. ( A ) Influence of free donor or free acceptor in the sample. Theoretical S-E histogram with trajectoriescorresponding to the addition of free donor or free acceptor to a construct with 1:1 donor to acceptor ratio. ( B ) Experimentalhistogram of S versus E for constructs showing different FRET values (C32V and C5V) or different stoichiometries (CVC andVCV) as well as pure donor (Cerulean) and pure acceptor (Venus). This histogram was calculated using only the crosstalkcorrection. ( C ). The same experimental E-S histogram with the complete calibration including γ M and β X . In the completelycorrected 2D histogram, the stoichiometry and FRET probability are uncorrelated ( ρ = . D ) Exemplary triplet of imagesshowing a cell expressing C32V with a low signal-to-noise ratio, Scale bar 15 µ m. ( E ) The corresponding RAW E and S mapsand the FRET map for the images in panel D after filtering with the weigthed gaussian filter. ( F ) The correspondingstoichiometry histogram and the weights (W) as a function of the stoichiometry (line). The weights are given, for each pixel, bya gaussian function of the deviation from the expected stoichiometry ( S = .
5) with a variance σ S = .
1. The correspondingmap of weights W is shown in ( G ). ( H ) Line profiles corresponding to the three maps shown in panel E . Due to high intensitybackground in an endosome, the FRET efficiency drops (thin grey line). This anomaly is also observable in the stoichiometry(blue). By weighting the image with the measured stoichiometry, such artifacts can be avoided (magenta).. e can then write the analytical formula describing this mix in the E-S histogram: S app = E / E app / S + E / E app − , (15)which is sketched in Fig.3A. In equations (2) and (3), we assumed that all the donors were able to FRET i.e. , had an acceptorpartner. If this is not the case and free donors exist, then E becomes an apparent FRET probability E app as in equation (14). Ifthe experimental E-S histogram can be fitted to equation (15), the FRET probability, E of the 1:1 construct can be extracted.The presence of free donors can result from the poor efficiency of the acceptor fluorophore to fold. As demonstrated above,this case can easily be seen and treated with the QuanTI-FRET method. The presence of free acceptors does not affect theFRET efficiency once the system calibrated. If free acceptors are present in the calibration samples, one should at least evaluateand take into account the effective stoichiometry in order to obtain a reliable calibration and avoid the propagation of biasesto the measurements of interest. If both free donors and free acceptors are present, the situation is more complicated due theensemble measurement made in each pixel. But fortunately, most of FRET-based biosensors are formed with variants of GFP,in particular of the pair CFP/YFP, which fold well .The observation of the E-S 2D histogram gives a hint about the quality of the calibration. In theory, for a sample with afixed stoichiometry, the FRET probability and the stoichiometry should be uncorrelated resulting in horizontal clouds in the 2Dhistogram. Figure 3B shows the experimental data from this work with crosstalk correction but with β X and γ M both set equalto 1. The constructs C5V and C32V do not lie on a horizontal line whereas they should have the same stoichiometry. On thecontrary, with the complete calibration of β X and γ M (Fig. 3C), the two clouds lie on a horizontal line corresponding to S = . ρ = .
02 for C5V-C17V-C32V).Once the system has been calibrated with FRET probes with a known stoichiometry, the stoichiometry becomes an outputof the QuanTi-FRET analysis. Two additional FRET standards were imaged under the same conditions as before, CVC (2donors:1 acceptor) and VCV (1 donor:2 acceptors) . As these two constructs were not used to determinate γ M and β X , noassumption was made with respect to their stoichiometry. Both constructs were built with the same fluorophore pair and imagedusing the same conditions (filter set, laser power, camera), hence, the calibration was still valid. Practically, the experimentalresults gave S = . ± . S = . ± . S = ±
4, 12 cells) as expected and the donor population is also found where expected at stoichiometry closeto 1 ( S = . ± .
4, 10 cells).In the case of a fixed stoichiometry sample, as is the case for most FRET-based biosensors, S can still bring an importantpiece of information about the confidence. The usual way to determine the uncertainty about a pixel is to rely on the photonstatistics: if the fluorescence signal is high, then a high confidence is assumed. This is certainly true for pure fluorescenceimaging but, in the case of FRET, there are cases where a high fluorescence intensity occurs in pixels where the FRET is biased.For instance, FRET can be affected by the local chemical environment (pH), the local crowding or by any unequal effect onthe fluorescence of the donor and acceptor. An example is shown on Figure 3D where lower-than-expected FRET efficiencywas observed in certain bright intracellular vesicles. The corresponding raw results of the pixel-based analysis is shown inFig.3E ( S RAW and E RAW ) and line profiles are plotted (Fig.3H). For this example, the spot pointed to by the arrow has a highfluorescence intensity in the three channels but the stoichiometry differs from the expected 50% (close to 65%). Similarly, dark,out-of-cell regions of the image also show deviation from the expected stoichiometry. We define a confidence index W as: W = e − ( S − S ) σ S , (16)where S is the expected S and σ S is a parameter to tune the sensitivity. W renders the deviation from an expectedstoichiometry as a score between 0 and 1 ( S = S ) with a gaussian shape (Fig.3F). This confidence index can be used directly todisplay FRET maps with color-coded FRET values and brigthness-coded W . To go one step further, the confidence index canbe inserted in a spatial filter. Indeed, FRET maps often need to be spatially averaged, the actual resolution being limited by thediffusion of the FRET species and larger than the pixel size. A weighted gaussian filter was therefore designed where the effectof a gaussian kernel (typically 7x7 pixels ) was locally weigthed with W (Fig.3G) as follows: E filt = ( W ◦ E ) ∗ GW ∗ G , (17)where ∗ denotes a convolution and ◦ the Hadamard product, E and W are dealt as matrices corresponding to the raw FRETimage and the weights as defined in equation (16), E filt being the filtered FRET map. As the gaussian distribution never reaches X γ M C5V C17V C32VQuanTI-FRET 1 . ± .
008 2 . ± .
02 50 . ± . . ± . . ± . . ± .
01 2 . ± .
05 47 . ± . . ± . . ± . . ± .
005 2 . ± .
02 49 . ± . . ± . . ± . Table 1.
Systematic comparison of QuanTI-FRET method with previous work from Lee et al. and Chen et al. Dataset [A]was analyzed with the three methods, the resulting correction factors and FRET probabilities for C5V , C17V and C32V aregiven in this table, with the uncertainty on β X and γ M resulting from a different bootstrap analysis.zero, an additional threshold was applied based on the local weight of the considered pixel. An example is shown on Figure3E,the application of the weighted gaussian filter ( σ S = . , σ Gauss = . W th = .
5) totally eliminates thebackground around the cells and also very dim areas inside cells as well as the bright vesicle with anomalous stoichiometry(Fig.3H).
Discussion
The definitions of FRET probability and stoichiometry used in QuanTI-FRET are mathematically equivalent to what wasintroduced previously by Chen et al. ( γ M ≡ G and β X ≡ / ( G · k ) ) and Lee et al. ( γ M ≡ γ and β X ≡ β ). Therefore,we compared the performances of QuanTI-FRET to these two particular other methods. In the work by Chen et al. , thephysical origin of the parameters was not described in detail as γ M was already introduced by Zal and Gascoigne and thesecond parameter, k , was rationally defined from the γ M -corrected intensities to account for the stoichiometry. The proposedcalibration was achieved in two separated steps. First, two constructs with defined and well-separated FRET efficiencies wereneeded to determine γ M (a.k.a G ). Second, a FRET standard with known stoichiometry was measured to calculate the otherparameter, k , using G determined in step 1. In Chen’s work, the calibration was achieved by imaging the FRET standardsC5V and CTV, where the linker T is the 229 amino-acid TRAF domain of the TRAF2 protein . However, the observation ofthe 3D representation of all the standards, including CTV, imaged in the present work, shows that CTV does not lie on thesame plane as C5V, C17V and C32V (Supplementary Fig.S5). This is also visible in the E-S 2D histogram where the CTVcloud is tilted (Supplementary Fig.S5). These observations are in agreement with the later work of Koushik and Vogel anddemonstrate the utility of the 3D representation of the fluorescence intensities as well as the E-S 2D histogram to proofreadthe quality of the experimental data. The analysis of the experimental dataset [A] with Chen’s method gave results close tothe QuanTI-FRET method: G = . ± .
02 to compare with γ M = . ± .
02 and 1 / ( G · k ) = . ± .
005 to comparewith β X = . ± .
008 (see Table 1). However, the analysis of the second dataset [B] gave different results between thetwo methods: G = . ± γ M = . ± .
07 and 1 / ( G · k ) = . ± β X = . ± . G and k is less robust than the single-step fit of the QuanTi-FRET method. In the work of Lee et al. , the calibration consistsof first calculating E raw and S raw with only spectral crosstalk corrections and then fitting the linear relation between 1 / S raw and E raw , hereby assuming a 1:1 stoichiometry (see Supplementary Information). This method yielded very similar results toQuanTI-FRET: γ = . ± .
05 to compare with γ M = . ± .
02 and β = . ± .
01 to compare with β X = . ± . ∆ E = ∆ E =
8% with a relative difference of 11% for β X and 28% for γ M . The correction factors and resulting FRET for the three FRET standards are summarized in Table 1. The average FRETprobabilities are in very good agreement between QuanTI-FRET and Chen’s methods, a systematic difference of about 3% isobserved with Lee’s method. The three methods can all be considered as quantitative.To further test the relative robustness of the three methods, a systematic bootstrap testing on experimental data ([A] withC5V, C17V and C32V) was performed. The whole experimental dataset was randomly divided to produce artificially smallerdatasets and give access to statistical errors on the correction factors determination (as given so far). The standard deviation of γ M was around 0.12 (QuanTI-FRET and Chen’s) and 0.23 (Lee’s) for the minimum tested sample sizes between 1000 and 1300points. The standard deviation of β X was found to be around 0.04 (QuanTI-FRET and Chen’s) and 0.07 (Lee’s) for the samerange of sample sizes. Over the whole range of sample sizes (from 10 to 10 ), the standard deviation of both correction factorsobtained by Lee’s method remained larger than the ones obtained by Chen’s and QuanTI-FRET (see Supplementary Fig.S6).This analysis demonstrates that Lee’s method is less robust to dataset length, probably due to the fitting of 1 / S which divergesfor small S values.A different test was performed by reducing the FRET range of the calibration dataset by taking alternatively only twostandards (C5V-C17V, C17V-C32V and C5V-C32V) into account. In this case, Chen’s method was not valid anymore for G and 38% for β X (see Supplementary Fig.S6).Indeed, Chen’s method relies purely on the comparison between the average intensities of two populations, the uncertaintygrows as the FRET distance decreases. QuanTI-FRET and Lee’s methods, by fitting the total distribution, perform well inthis bench test (relative variations of 14% and 22% for γ M respectively with QuanTI-FRET and Chen’s, and 7% and 12%respectively for β X , see Supplementary Fig.S5).All in all, even if the three methods are quantitative in the best case scenario, QuanTI-FRET was demonstrated to be morerobust to dataset dispersity, length and FRET range. The single-step calibration in a 3D I DD , I corrDA , I AA representation, on acontinuous distribution of FRET efficiencies allows for the calibration on-the-fly of the sample of interest itself, provided adefined stoichiometry and a distribution of FRET efficiencies in the range of the bench test (at least 5 %). Taking inspirationfrom single-molecule literature, we can further exploit stoichiometry to provide a quality check of the experimental data andthereby filter the resulting FRET images. Conclusion
Building upon the previous contributions from live-cell and single-molecule FRET experiments, we present a new frameworkallowing for quantitative FRET imaging in living cells with a simple multi-channel epifluorescence microscope. Here, wedemonstrated the consistency of the method on two different microscopy systems in different laboratories. The QuanTI-FRETmethod does not require specific instrument for determining spectra or lifetime nor specific hardware development. Image-splitting devices and LED excitation are now commercially available and allow for the same image acquisition protocols asthe experimental system used in this work. The QuanTI-FRET calibration does not require acceptor photobleaching, purifiedproteins or known FRET samples. The only requirement is a known stoichiometry sample (as other quantitative methods) witha broad FRET distribution, which can be obtained directly from the FRET construct of interest (intramolecular-FRET-basedbiosensors for instance). Nevertheless, an independent calibration using FRET standards is recommended as it allows one toevaluate FRET efficiency and stoichiometry independently. The QuanTI-FRET method was demonstrated to be quantitativeand robust, with the additional benefit of having an inherent data quality check.
Methods
Cells and plasmids
All plasmids were gifts from Steven Vogel: C5V (Addgene plasmid
E.Coli (DH5 α ) and purified using the NucleoBond R (cid:13) TM (Gibco TM ) and Penicillin/ Streptomycin (1%). Cells were transfected with Lipofectamine R (cid:13) TM ) and Opti-MEM (Gibco TM ), then incubated in Fluorobrite DMEM medium (Gibco TM ) overnight and finallyimaged in Leibovitz’s L-15 medium (Gibco TM ) without phenol red. Microscopic image acquisition, Grenoble, setup [A]
Imaging was done with a system based on an Olympus IX83 body equipped with a home-made image splitting coupled to asCMOS camera (ORCA Flash V2, Hamamatsu) as sketched in Fig.1. Excitation was done by a supercontinuum white laser(Fianium) coupled to a high power AOTF (Fianium), which was controlled through an FPGA-RT unit (National Instruments)coded with Labview. This unit synchronized the alternated laser excitation with the camera acquisition. Images were acquiredat 37 ◦ C with Micromanager and a 40x objective. The donor fluorophore was excited at 442nm, the acceptor at 515nm. Thefluorescence emission was first separated from the excitation via a triple line beamsplitter (Brightline R442/514/561 Semrock)in the microscope body. The fluorescence emission was further splitted with a beamsplitter at 510nm (Chroma) and filteredwith a 475/50 filter (BrightLine HC, Semrock) for the donor channel and a 519/LP longpass filter (BrightLine HC, Semrock)for the acceptor channel. Hence, in two camera snapshots, four images were obtained with all combinations of donor/acceptorexcitation and donor/acceptor emission.
Microscopic image acquisition, Munich, setup [B]
Images were acquired on a Nikon Eclipse Ti microscope with home-built excitation and detection pathways. A 100x oilimmersion objective (Apo-TIRF 100x Oil/NA 1.49, Nikon) was used for all measurements. Samples were excited with 445nm(MLD, Cobolt) and 514nm (Fandango, Cobolt) diode lasers coupled to an AOTF (PCAOM LFVIS5, Gooch & Housego)controlled by a FPGA unit (cRIO-9074, National Instruments). The fluorescence emission was separated from excitationpathway with a triple line 445/514/594 beamsplitter. The donor and acceptor emission were separated using an additional514LP beamsplitter and were then spectrally filtered using 480/40 and 555/55 bandpass filters respectively before being detected n separate EMCCD cameras (DU-897, Andor). Each cell was excited for 300 ms at 445 nm followed by 300 ms at 514 nm.The camera exposure was synchronized to laser excitation through the FPGA unit and a self-written Labview program. Thisproduced four images over two exposure periods capturing donor and acceptor emissions at each excitation wavelength.
Image analysis
All the image analysis calculations were coded in Python, figures and plots were done in Python except for the boxplotsobtained with PlotofPlots . Raw fluorescence images were pre-treated by substracting the dark count of the camera andflattened by dividing with a fluorescence image obtained from a uniform fluorescent sample (Chroma slide). An essential stepis then the registration between the two channels obtained on each half of the camera or between cameras. Brightfield imagesof beads randomly and densely spread on a coverslip were used for calibration. By calculating the image cross-correlations inlocal regions of the image between the two channels, a displacement map was obtained and hence a transformation matrix wascalculated (accounting for translation, rotation, shear and magnification). This transformation matrix was systematically appliedto I DD to match I DA and I AA before any calculation. Calibration of the system with QuanTI-FRET was done as explained in themain text. Visualization of the 3D fit was done in Paraview to explore all view angles. All calculations were done pixelwise.Parameters for the weighted gaussian filter are chosen as for gaussian filtering depending on the pixel intensity. Here, thespatial filtering is principally used to filter out pixels with an aberrant stoichiometry, i.e. S larger than 0.6 or smaller than 0.4 asestimated from the S-E histograms. The spatial gaussian enveloppe is designed to avoid adding noise in this operation, as S issubjected to stochastic pixel-to-pixel noise as E .The data that support the findings of this study are available from the corresponding author upon reasonable request. References Ha, T. et al.
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The authors are grateful to S. Pinel and N. Scaramozzino (M2Bio platform) for advices and help in plasmid amplification andpurification. We thank B. Arnal and I. Wang for fruitful discussions and numerical advices. P.Moreau is acknowledged for histechnical participation in building and maintaining the setup. This work was funded by the Agence Nationale de la Recherche(ANR, grant n ◦ ANR-13-PDOC-0022-01), and supported by the Université Grenoble Alpes (UGA, AGIR-POLE program 2015,project ACTSUB). C.M.B., A.C. and A.D. are part of the GDR 3070 CellTiss. D.C.L. gratefully acknowledges the financialsupport of the Deutsche Forschungsgemeinschaft (DFG) via the collaborative research center (SFB1035, Project A11) and theLudwig-Maximilians-Universität through the Center for NanoScience (CeNS) and the BioImaging Network (BIN). CAR andCO are supported by FRM and ANR (CE17 CE13 0022 01). uthor contributions statement
A.D. conceived the experiments and the theory. D.C.L contributed to the concept. C.O and C.A-R contributed to the design ofthe biological protocols. A.C., C.M.B, C.Q. conducted the experiments. A.D and A.C analyzed the results. F.W. and C.M.Bbuilt and interfaced the hardware. A.D drafted the manuscript. All authors reviewed the manuscript and approved the finalversion.
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