Non-fitting approaches

1. mf_D.

The minimal fraction of interacting donor mf_D was introduced by us in 2008 [14]. Briefly, if the donor intensity decay is mono-exponential (i.e. eGFP or mTFP1 [25]); a two populations system (FRET and no-FRET species) with a narrow distribution of FRET efficiencies can be assumed when FRET occurs. In this case a bi-exponential intensity decay can be employed to describe the fluorescence decay (cf. Eq. 1) and the minimal fraction of interacting donor is given by(3)where <τ> is the mean lifetime defined by

(4)This parameter has already been exhaustively compared with the true fraction of interacting donor (f_D) in [14]. Briefly, as indicated in Fig. 1A, mf_D is equal to f_D only for one particular FRET lifetime τ_F (indeed when τ_F = <τ>/2) but the error between mf_D and f_D remains confined for a relatively large range of τ_F (around 500 ps).

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Figure 1. Theoretical fractions of interacting donor calculated with the polar approach f_D^P or the moments method f_D^M (in black) and theoretical mf_D values (in red) as a function of the lifetime of the donor in presence of the acceptor τ_F (for a donor lifetime of 2.5 ns).

Three distinct f_D values were considered in (A). We have also plotted the means in (B) and the standard deviations in (C) of f_D^P in black (deduced from Eqs. 15 and 16), those of f_D^M in blue (deduced from Eqs. 18 and 19) and those of mf_D in red (deduced from Eqs. 13 and 14) as a function of the total number of photons N. The following FRET parameters were used: τ_F = 1.5 ns, τ_D = 2.5n s and f_D = 0.25, 0.5 and 0.75.

https://doi.org/10.1371/journal.pone.0069335.g001

1. Polar approach.

The theory of the polar approach for TD FLIM experiments has been detailed previously [16], [26]. Briefly, each acquired intensity histogram in TD FLIM experiments is converted into [u;v] coordinates. These u and v coordinates are respectively the cosine and sine transforms of the fluorescence intensity decay p(t) which are defined by(5)(6)where ω is the laser repetition angular frequency.

Recently, we have demonstrated that it is possible to retrieve quantitatively the FRET parameters from these polar coordinates [22]. In fact, for a bi-exponential intensity decay (and in the case of a single exponential donor), the fraction of interacting donor f_D and the fluorescence lifetime of the donor in presence of the acceptor τ_F can be analytically expressed as(7)(8)

We have represented this analytical fraction of interacting donor as a function of τ_F in Fig. 1A and we can clearly notice that the analytical f_D^P corresponds exactly to the true f_D for all lifetime values τ_F comprised between 0 and τ_D.

1. Moments method.

We propose an alternative method for estimating the fraction of interacting donor f_D and the fluorescence lifetime of the donor in presence of the acceptor τ_F for a bi-exponential intensity decay. Our method is based on the calculation of the moments of the first and second order which are defined by(9)(10)

By simply resolving the system of equations 9 and 10, a straightforward calculation leads to(11)(12)

The analytical fraction of interacting donor f_D^M is represented as a function of τ_F in Fig. 1A; it is equal to the true fraction of interacting donor when the lifetime τ_F is comprised between 0 and τ_D.

Monte Carlo Simulations

For generating TD FLIM images with controlled parameters, we have performed Monte Carlo simulations on a standard computer. More details on the algorithm can be found in [27], [28]. In order to be as close as possible of the experimental conditions, we consider a laser repetition frequency of 80 MHz which corresponds to a total window width of 12.5 ns. All the simulated inte ity decays consist of two components whose lifetimes are respectively τ_F = 1.5ns and τ_D = 2.5 ns and three distinct fractions of interacting donor were used f_D = 0.25; 0.5 and 0.75. For each condition, we have simulated a FLIM image of 64×64 pixels corresponding to 4096 intensity decays and each simulated decay is composed of N photons divided into N_ch temporal channels.In this work, we have simulated lifetime images acquired with two largely used TD FLIM systems: the time correlated single photon counting (TCSPC) and the time gated system. For TCSPC simulations, the measurement window which is divided into 64 temporal channels is limited to 12.5 ns and the offset is neglected because it is generally less than few photons per pixel. The full width half maximum (FWHM) of the simulated Gaussian instrumental response function (IRF) with the TCSPC technique is fixed to 32 ps, as measured by Waharte et al. [12]. For time gated simulations, we consider that the measurement window of 12.5 ns is divided into N_ch contiguous gates with variable width w = 12.5/N_ch. The FWHM of the simulated IRF is fixed to 200 ps corresponding to the measured rising time of our time gated system. To simulate the intensifier noise, we added to each pixel a Poisson distributed offset of 190 photons (corresponding to 1600 grey levels in our time gated system). The simulated FLIM images are finally smoothed with a 3×3 average filter in order to obtain a comparable signal to noise ratio than those of our time gated system. For investigating the performance of all FLIM image analysis strategies during fast-FLIM FRET experiments, we have considered several total numbers of photons N and several numbers of gates N_ch.

Experimental Setup

Our fast-FLIM system combines a supercontinuum laser, a spinning disk system to improve spatial resolution and provide optical sectioning and a fast-gated intensifier coupled to a CCD camera for rapid FLIM acquisition (Fig. 2). The supercontinuum laser (Fianium SC400-6) provides a wide spectrum from 400 to 2400 nm with a high power in the visible range (3 mW/nm) which is well adapted for FLIM measurements when it is combined with a multifocal system. The multifocal illumination of the sample is performed by a spinning disk system (Yokogawa CSU-X1) implemented on an inverted microscope (Leica DMI6000). The excitation light is spectrally filtered before illuminating the sample through an oil immersion objective (100×, NA 1.4, Leica). The fluorescence decay is acquired with a CCD camera (CoolSnap hq², Photometrics) coupled to a fast gated intensifier (PicoStar, LaVision, Kentech Instruments) triggered with an electronic signal coming from the laser. This electronic signal is sequentially delayed by a programmable delay generator for obtaining a stack of time-correlated images. Each image which corresponds to a temporal width of 2.25 ns is acquired with an exposure time that usually varies between 20 and 100 ms. Our system is fully controlled by MetaMorph (Molecular Devices) and the FLIM acquisitions are driven by a homemade MetaMorph program (Flimager) that calculates the mean lifetime (cf. Eq. 4) on-line from a background-subtracted and smoothened (with a 3×3 average filter) fluorescence stack of images and provides a FLIM acquisition rate up to 1 image/s allowing to follow the spatio-temporal evolution of the protein-protein interactions occurring in the sample.

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Figure 2. Fast-FLIM scheme.

The supercontinuum laser is collimated out of the fiber, spectrally filtered (473–491 nm) and injected into the Yokogawa spinning disk system where shaping optics extend the beam. The micro-lenses disk creates a multitude of beams focused in the pinholes of the coupled disk conjugated with the sample plane. The emitted fluorescence is selected by a dichroic mirror DM (transmission peak at 488 nm) and an emission filter (500–550 nm), and converted into electrons with the photocathode of the intensifier. Each laser pulse triggers the photocathode so that it runs as an ultra-fast shutter (time gate of 2.25 ns at 80 MHz). The electrons are amplified by a micro channel plate and converted back into light with a phosphorescent screen. The photons are finally acquired with a CCD camera (with binning 3×3) and the fluorescent images are saved. A home-made MetaMorph user program called Flimager (MFQ, IGDR) was developed for both controlling the complete system (delay generator, CCD camera and microscope), and calculating the FLIM images on-line.

https://doi.org/10.1371/journal.pone.0069335.g002

FLIM Image Analysis

For analyzing the TD-FLIM images with the standard fitting method, we have used the well known least square method (with Levenberg-Marquardt algorithm) for minimizing the difference between the experimental data and the theoretical model [29]. All temporal histograms were fitted with a two components exponential model and the first lifetime τ_D was fixed to the donor lifetime (which is equal to 2.5 ns for the simulated FLIM images). The following parameter constraints (min lifetime: 0 ns; max lifetime: 2.5 ns; max ratio: 1) and standard algorithmic settings (10 iterations, Δχ² = 0.001) were used.

The TD FLIM images have also been analyzed with a custom-made software named MAPI (IRI, USR 3078 CNRS, BCF, available on request: http://biophotonique.univ-lille1.fr/spip.php?rubrique60) for investigating the performance of the non-fitting methods (mf_D, polar approach and moments method). This software allows computing the Fourier sine and cosine transforms of all temporal histograms and calculating the proportion of interacting donor and the donor lifetime in presence of the acceptor deduced from both the polar approach (cf. Eqs. 7 and 8) and the moments method (cf. Eqs. 11 and 12) when the donor lifetime is fixed. MAPI software was also used for calculating the mf_D value from Eq. 3 (which requires also fixing the donor lifetime). To obtain correct values, we need that intensity decays are background corrected. To do this, we estimate an average background from a non fluorescent region of interest that we subtract from the temporal histograms.

Solutions, Cell Culture and Transfection

A first solution containing Rhodamine 6G (Rd6G) at a concentration of 5×10⁻⁶ M and potassium iodide (KI) at a concentration of 0.025 M was prepared (50% water and 50% ethanol). A second solution of Acridine Orange (AO) at a concentration of 5×10⁻⁶ M and potassium iodide (KI) at a concentration of 0.025 M was prepared (50% water and 50% ethanol). The fluorescence lifetimes of these two solutions were measured with our TD-FLIM system. We found respectively 2.54 ns for Rd6G and 1.66 ns for AO; these values are used for mimicking the lifetime of the donor alone and the lifetime of the donor when FRET occurs. The excitation and emission spectra of both solutions measured with a spectrofluorimeter (Fluorolog, Horiba Jobin Yvon) are presented in Figure S3 showing that both dyes were efficiently excited at an excitation wavelength of 488 nm. In order to simulate a FRET system with different fractions of interacting donor, we produced different mixtures of the pure solutions of Rd6G and AO: 90/10, 70/30 and 50/50. The real f_D contribution for each mixture has been calculated by taking into account the pre-exponential factor coming from each pure fluorescence decay (a = I/τ where I corresponds to the total integral intensity and τ is the fluorescence lifetime), we found f_D = 0.17, 0.44 and 0.65.

3T3 cells were cultured in Dulbecco’s modified Eagle’s medium containing 10% fetal bovine serum (PAA Laboratories GmbH, Pasching, Austria). The cultures were incubated at 37°C in a humidified atmosphere of 5% CO2. 3T3 cells were seeded on Mattek coverslips at a density of 2×10⁵ cells. When cells reached 70% confluence, they were transfected with a total amount of 1 µg of expression vectors (either Rac-GFP+mCherry (negative control) or Rac-GFP+PBD-mCherry [30]) using Nanofectin I (PAA). Twenty-four hours after transfection, cell medium was changed. A special DMEM-F12 medium was used to prevent auto-fluorescence (DMEM-F12 without phenol red, B12 vitamin, riboflavin and supplemented with 20 mM HEPES and L-Glutamine from PAA).

Standard Fitting Method for Low Numbers of Photons

The fitting method remains the most common strategy for determining FRET parameters from TD-FLIM images [1], [29], [31]. In order to investigate the performance of this standard fitting method, specifically when the number of photons is low, we have simulated bi-exponential intensity decays (with a donor lifetime of 2.5 ns, a donor lifetime in presence of the acceptor of 1.5 ns and a fraction of interacting donors of 0.25, 0.5 and 0.75) with a constant number of temporal channels (N_ch = 64) and different total numbers of photons (N = 100000, 1000 or 200) acquired with TCSPC technique. In order to improve the estimation of the FRET parameters (and for a fair comparison with non-fitting strategies), we have reduced the number of unknown parameters in Eq. 1 by fixing the donor lifetime to 2.5 ns. We have investigated the effect of modifying the initial parameters (f_D and τ_F) on the estimated FRET parameters with the standard fitting method. The results reported in Fig. 3 indicate that the FRET parameters estimated by the standard fitting method are dependent on the initial conditions when the amount of counted photons is reduced. For instance, for N = 200 photons, the standard fitting method is able to estimate correctly both FRET parameters (f_D and τ_F) if the initial conditions are: f_D = 0.5 and τ_F = 1.5 ns. In other words, we need to know the FRET parameters in order to estimate them correctly with the standard fitting method when the number of photons is low, which is not appropriate for automated analysis of FRET-FLIM experiments.

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Figure 3. Importance of the initial conditions for the standard fitting method for three distinct total numbers of photons: 200 (in light gray), 1000 (in dark gray) and 100000 (in black).

We have considered three fractions of interacting donor f_D: 0.25 (A), 0.5 (B) and 0.75 (C). The minimal fractions of interacting donor are plotted in the left part and the lifetimes of the donor in presence of the acceptor in the right part. For each condition, the dotted lines represent the simulated values and the markers with error bars represent the medians and interquartile ranges of 4096 simulated TCSPC histograms (with τ_F = 1.5 ns, τ_D = 2.5 ns and N_ch = 64 channels).

https://doi.org/10.1371/journal.pone.0069335.g003

Theoretical Comparison of the Non-fitting Strategies as a Function of the Number of Photons

For investigating the performance of all non-fitting strategies, we have calculated the means µ, and the standard deviations σ, of each method as a function of the number of photons N, based on the exhaustive work performed by Philip & Carlson [32]. For mf_D, we obtain (cf Text S1)(13)(14)

For τ_D = 2.5 ns and τ_F = 1.5 ns, we have plotted in Fig. 1B and C, the means and the standard deviations of mf_D as a function of the number of photons N for three distinct fractions of interacting donor (f_D = 0.25, 0.5 and 0.75). As expected, the standard deviations decrease when the number of photons increases and the means converge rapidly to the theoretical value of mf_D (obtained for N→∞). For example, the differences between the theoretical and the calculated expectations of mf_D are less than 0.05 when the number of photons N is more than 120 photons (for the three considered fractions of interacting donor). However, as previously explained, we emphasize the fact that these theoretical and calculated expectations of mf_D underestimate the true f_D values.

We proceed in the same way as previously described for calculating the mean and the standard deviation of f_D^P; we obtain(15)(16)where we introduce the notations

(17)For τ_D = 2.5 ns and τ_F = 1.5 ns, Fig. 1B and C show the variations of the means and the standard deviations of f_D^P versus the number of photons N for the same three fractions of interacting donors. We notice that the means converge rapidly to the theoretical values (obtained for N→∞) since the differences between the calculated and the theoretical expectations of f_D are less than 0.05 when the number of photons is above 140. In the same way as for mf_D, the standard deviations of f_D^P decrease monotonously when N increases and we remark that the standard deviations of f_D^P are larger than those of mf_D. However, in contrast with mf_D it is important to notice that the calculated expectations of f_D^P correspond to the true f_D values.

We have finally investigated the performance of the analytical f_D^M when the number of photons is low. By applying the same procedure as previously described, we found the mean and the standard deviation of f_D^M(18)(19)

Using τ_D = 2.5 ns and τ_F = 1.5 ns, the variations of the means and the standard deviations of f_D^M as a function of the number of photons are represented respectively in Fig. 1B and C. For each fraction of interacting donor (f_D = 0.25, 0.5 and 0.75), we show that the means converge more rapidly to the theoretical values than the polar approach. For instance, the differences between the calculated and the theoretical expectations of f_D are less than 0.05 when the number of photons is above 100. The standard deviations of f_D^M are also slightly reduced in comparison with those of f_D^P, suggesting that the moments method should be more accurate than the polar approach.

Comparison between the Non-fitting Strategies as a Function of the Number of Photons

In order to investigate the performance of all non-fitting methods (mf_D, polar approach and moments method) when the number of photons is low, we have simulated bi-exponential intensity decays with a donor lifetime of 2.5 ns, a donor lifetime in presence of the acceptor of 1.5 ns and with distinct fractions of interacting donors 0.25, 0.5 and 0.75. We have first considered a constant number of temporal channels of 64 with different number of counted photons, varying from 100 to 1000 acquired with the TCSPC technique. The results presented in Fig. 4 indicate as expected that the calculated mf_D underestimates the true f_D for 0.5 and 0.75 but the difference between both values does not exceed 0.09 for all considered fractions of interacting donor. Furthermore, as anticipated from the theory when N≥200 photons, the polar approach gives reliable and unbiased fractions of interacting donor f_D^P and lifetime values τ_F^P with an expected increased interquartile range when the number of photons decreases. Indeed, for the same previous example (N = 200 photons and f_D = 0.25), the difference between the estimated and the simulated f_D is 0.08 and the difference between the estimated and the simulated τ_F is around 50 ps. The average lifetime remains also accurate for all considered conditions. Finally, with the proposed moments method, the accuracy and precision of both FRET parameters (f_D^M and τ_F^M) are theoretically expected to be improved in comparison with the polar approach. This is the case for f_D = 0.5 and 0.75 and particularly when the number of photons is high. For instance, for N = 1000 photons and f_D = 0.75, the difference between the estimated and the simulated f_D is 0.02 and the difference between the estimated and the simulated τ_F is 40 ps. Furthermore, the interquartile ranges of f_D^M and τ_F^M which are respectively 0.06 and 0.12 ns are reduced compared to those of f_D^P and τ_F^P which are equal to 0.08 and 0.18 ns. However this is no longer true for f_D = 0.25. In this condition, the difference between the estimated and the simulated τ_F increases when N decreases and it becomes greater than 450 ps for the previous example (N = 200 and f_D = 0.25). This discrepancy may be explained by the fact that the second order moment is not defined by a unique positive real root close to the limit conditions (low N, N_ch or small f_D), which lead to biased f_D^M and τ_F^M values.

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Figure 4. Comparison of the performance of the non-fitting strategies as a function of the total number of photons for three distinct fractions of interacting donor f_D: 0.25 (A), 0.5 (B) and 0.75 (C).

The polar approach is indicated in black, the moments method in blue and the mf_D in red. For all methods, we have reported the estimated f_D and the estimated mf_D value in the left part of the figure. The estimated donor lifetime in presence of the acceptor τ_F, and the estimated mean lifetime <τ> are reported in the right part. In all cases, medians are indicated with markers and error bars correspond to the interquartile ranges of 4096 simulated histograms whose parameters are: τ_F = 1.5 ns, τ_D = 2.5 ns and N_ch = 64 channels (TCSPC simulations) and the simulated values are indicated in dotted lines.

https://doi.org/10.1371/journal.pone.0069335.g004

From these Monte Carlo simulations, the non-fitting strategies appear robust for estimating FRET parameters (f_D and τ_F) when the number of photons is low (except for the moments method). However, they do not permit accurate estimation of FRET parameters when the number of photons becomes less than 200.

Comparison between Non-fitting Strategies as a Function of the Number of Temporal Channels

If the number of photons cannot be reduced, the last solution for accelerating the acquisition time of FLIM-FRET experiments is to decrease the number of temporal channels of the time gated FLIM system (fast-FLIM prototype). Indeed, the principle of the time gated FLIM system consists of collecting (for each temporal channel) the fluorescence emitted by the sample during the selected gate width until the desired acquisition time is reached. The total acquisition time is then simply given by the product of the number of channels and the acquisition time for one channel. Consequently, a basic reduction of the number of channels allows speeding up the total acquisition time while maintaining constant the total number of photons (if the gates are contiguous and their width is adapted to the total measurement window). However this reduction of channels degrades also the accuracy of the FRET parameters estimated with non-fitting strategies (cf. Fig. S1).

The poor performance of all non-fitting strategies (mf_D, polar approach and moments method) can be explained by the fact that these strategies are entirely based on the calculation of either the [u;v] coordinates or the moments E{τ}, E{τ²} which are all theoretically defined with integrals (cf. Eqs. 5, 6 and 9, 10). However, in practice, these integrals are numerically approximated because the intensity decays are constituted with a finite number of experimental points. Numerous methods are available for approximating finite integrals [33]. In this work, we use a polynomial of degree 1 as an interpolating function which means that the integrals are approximated with a sum of trapezoids. The corrected expressions obtained for all non-fitting strategies are reported in the supplementary material (texts S1, S2, S3 and S4).

For validating these corrected expressions, we have performed time gated simulations. We have simulated bi-exponential decays with the same previous parameters (τ_D = 2.5 ns and f_D = 0.25, 0.5 and 0.75) and we have considered a fixed number of photons (N = 1000 photons corresponding to 8500 grey levels in our system) and distinct number of contiguous gates varying from 4 to 64. The FRET parameters calculated from the corrected expressions are reported in Fig. 5 for all non-fitting strategies. With our corrected expressions, both the mf_D and the polar approach allow correct estimation of the FRET parameters for all fractions of interacting donor. For instance, the difference between the calculated and the simulated f_D values is indeed less than 0.05 and the difference between the calculated and the simulated τ_F is less than 140 ps for all numbers of temporal channels (except for N_ch = 4). Furthermore, the difference between the calculated mf_D and the simulated f_D values is always less than 0.1 for all fractions of interacting donors, even if the number of temporal channels is as low as 4, confirming the fact that this non-fitting strategy is well adapted for estimating FRET parameters in fast-FLIM-FRET experiments.

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Figure 5. Performance of the non-fitting methods (polar approach in black, moments method in blue and mf_D in red) as a function of the number of temporal channels for N = 1000 photons (time gated simulations).

We have considered three fractions of interacting donor f_D: 0.25 (A), 0.5 (B) and 0.75 (C). τ_F and <τ> are reported in the right part whereas f_D^P, f_D^M and mf_D are indicated in the left. For each condition, the dotted lines represent the simulated values and the markers with error bars represent the corresponding medians and interquartile ranges of 4096 simulated histograms with parameters: τ_F = 1.5 ns and τ_D = 2.5 ns.

https://doi.org/10.1371/journal.pone.0069335.g005

Concerning the moments method, its domain of validity is reduced. As previously described, when f_D = 0.25, the difference between the calculated f_D^M and the simulated f_D values can reach 0.12 and the recovered τ_F^M is not correct. For instance, the difference between the calculated τ_F^M and the simulated τ_F can exceed 0.8 ns, which is not acceptable.

To complete this investigation and to validate the robustness of both polar approach and mf_D, additional Monte Carlo simulations were carried out in the same way (with contiguous gates varying from 4 to 64) by fixing now the number of photons to 200 (corresponding to 1700 grey levels in our time gated system). The results obtained with all non-fitting strategies are presented in Fig. 6. As expected, the moments method is not valid when f_D = 0.25 whatever the number of temporal channels is (the difference between the calculated f_D^M and the simulated f_D value can reach 0.22 and the difference between the calculated τ_F^M and the simulated τ_F is more than 1.78 ns). But surprisingly, when the number of gates is greater than 4, the moments method is reasonably valid for f_D = 0.5 and almost perfect when f_D = 0.75. The domain of validity of the moments method seems to be more affected by the f_D value than by the number of detected photons, even if the standard deviation increases when the number of photons decreases. Concerning the other non-fitting strategies (polar approach and mf_D), they stay accurate even with only 4 gates and 200 photons. For instance, the difference between the calculated and the simulated f_D values is less than 0.1 and the difference between the calculated and the simulated τ_F is less than 220 ps for all number of temporal channels (except for N_ch = 4). With mf_D, the difference between the calculated mf_D and the simulated f_D values is always less than 0.12. Furthermore, as predicted by the theory, we note that the standard deviations of mf_D are reduced in comparison with those of the polar approach. For example, for N_ch = 8 and f_D = 0.75, the interquartile range of mf_D (iqr = 0.04) is less than that of f_D^P which is equal to 0.11.

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Figure 6. Performance of the non-fitting methods (polar approach in black, moments method in blue and mf_D in red) as a function of the number of temporal channels for N = 200 photons acquired with time gated system.

Three fractions of interacting donor f_D are considered: 0.25 (A), 0.5 (B) and 0.75 (C). We have indicated the fraction of interacting donor and the mf_D in the left part; the donor lifetime in presence of the acceptor τ_F and the mean lifetime <τ> are in the right part. In all graphs, the dotted lines represent the simulated values and the markers with error bars represent the corresponding medians and interquartile ranges of 4096 simulated histograms whose parameters are: τ_F = 1.5 ns and τ_D = 2.5 ns.

https://doi.org/10.1371/journal.pone.0069335.g006

Comparison between Non-fitting Strategies on Experimental FLIM Measurements of Fluorescent Solutions using Fast-FLIM Prototype

In order to investigate the validity of the non-fitting strategies on experimental data, we have performed FLIM measurements of fluorophores solutions with our fast-FLIM prototype presented in Fig. 2. This time gated prototype was designed for fast acquisition of FLIM by using five gates of 2.25 ns width. We prepared three mixtures of two fluorophores, Rd6G and AO in the presence of KI in order to mimic the simulated lifetime values (see Material and Methods for details). We have acquired several FLIM images with different numbers of detected photons per pixel, N, varying from 200 to about 1600 (determined from S-factor quantification, see Fig. S2). These FLIM images were analyzed with all non-fitting strategies: mf_D, polar approach and moments method. The results are summarized in Fig. 7. Firstly, it has to be noted that the number of detected photons, N, does not influence the accuracy of the FRET parameters estimated with the non-fitting strategies. Secondly, when f_D = 0.17, the moments method is not valid (values of τ_F^M out of range). Even with the polar approach, τ_F^P is not accurate and the standard deviation is large. This could be easily explained in the graphical representation of the polar plot because the two dots corresponding respectively to the donor alone (Rd6G in white) and f_D = 0.17 (in blue) are close, meaning that the line construction with the interception of the semi-circle for recovering τ_F is not precise. Concerning the fraction of interacting donor, both strategies (mf_D and polar approach) correctly estimate this parameter, which is not the case with the moments method (unacceptable underestimation of the f_D value). Thirdly, for f_D = 0.44 and 0.65, we can notice that the f_D values are overestimated with the three non-fitting strategies but this discrepancy would probably come from the calculation of the theoretical f_D of the fluorescent solutions. This hypothesis is in agreement with the diminution of the estimated mean lifetime in comparison with the theoretical one shown in panels B1 and C1 of Fig. 7 since it is well known that the mean lifetime is a robust parameter [14], [34]. Excluding this difference, all non-fitting strategies are very robust for recovering τ_F and f_D even when using only 5 gates which was not evident from the simulated results of the moments method (5 is sufficient whereas 4 was not enough, see Fig. 5). Finally, we note that the standard deviations of the different non-fitting strategies are coherent with the theoretical predictions of Fig. 1. As expected, mf_D is the less noisy strategy and the moments method (when it is valid) exhibits a smaller error deviation than the polar approach (Panels E and F in Fig. 7).

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Figure 7. Experimental FLIM measurements on fluorescent solutions with our fast-FLIM prototype.

Lifetime images of Rd6G alone, AO alone and of three mixtures of Rd6G and AO with theoretical fractions of interacting donor of 0.17, 0.44 and 0.65 were acquired with N≈1500 photons. The polar plot and the mean lifetime images of each solution are represented in (A). All spots corresponding to the mixtures in the polar plot are well localized on a line connecting pure Rh6G and pure AO. We have also calculated f_D^P, f_D^M and mf_D for the three mixtures and the corresponding images are indicated in (B). We show in (C) the images of donor lifetime in presence of the acceptor estimated with the polar approach and the moment method. We have also performed FLIM acquisitions with different numbers of detected photons for each fraction of interacting donor: 0.17 (D), 0.44 (E) and 0.65 (F); the corresponding plots of f_D^P, f_D^M, mf_D, τ_F^P and τ_F^M as a function of N are reported in the right part. For all graphs, markers with error bars represent the medians and interquartile ranges of FLIM images. The theoretical f_D and τ_F are indicated in dotted lines.

https://doi.org/10.1371/journal.pone.0069335.g007

Spatio-temporal Quantification of Protein-protein Interactions in Living Cell Using Fast-FLIM Prototype and Non-fitting Approaches

To demonstrate the ability of the non-fitting strategies to probe protein-protein interactions in live cells by FRET with the fast-FLIM prototype, we applied them to the quantification of G protein activation in 3T3 cells [15], [24]. The Rho family of small GTPases regulates cell shape and motility. When Rac is in its active form (GTP bound state), it interacts with effectors that affect actin polymerization. The PBD assay allows detection of the active form of Rac (Fig. S4) and in our case, PBD-mCherry was expressed throughout the cell (meaning that no particular sub-localization was found). FLIM images of a 3T3 cell co-expressing Rac-GFP and PBD-mCherry and a cell co-expressing Rac-GFP+mCherry as a reference (negative control) were acquired with our fast-FLIM prototype. From the S-factor, we deduced that the detected mean numbers of photons were respectively 830 and 850 photons for the reference and the cell co-expressing Rac-GFP and PBD-mCherry. The FLIM images were then analyzed with all non-fitting strategies (mf_D, polar approach and moments method) and the results are reported in Fig. 8. Both, the polar plot (Fig. 8A) and the corrected mean lifetime (Fig. 8B) show a modification of the lifetime caused by FRET. Fig. 8B shows a global mean lifetime decrease of the cell co-expressing Rac-GFP and PBD-mCherry (<τ> = 2.21+/−0.06) relative to the control cell expressing Rac-GFP only in the presence of diffusing mCherry (<τ> = 2.40+/−0.07). This diminution was also observed in the whole population of analyzed cells; we found a mean lifetime <τ> = 2.42+/−0.03 ns (n = 10) for the negative control cells which decreases to 2.37+/−0.02 ns (n = 10) for the co-expressing cells (Fig. S4F). The fast-FLIM prototype offers the possibility of acquiring data very rapidly (in this case, 1 FLIM image per sec). Our aim is to analyze the spatio-temporal evolution of Rac activation for a small region of interest. We have then calculated the fraction of interacting donors with all non-fitting approaches (cf. Fig. 8C). Fig. 8C4 shows that mf_D, f_D^P and f_D^M have similar temporal oscillations which correspond to transient transitions of Rac between GDP and GTP forms. These oscillations indicate real Rac1-PBD interactions since such variations of mf_D, f_D^P and f_D^M are not present in cell co-expressing Rac-GFP+mCherry (cf. Fig. S5). Note that the values of mf_D and f_D^P are almost similar since for the typical range of lifetimes of the fluorescent proteins (around 2.5 ns) τ_F lifetimes are close to <τ>/2 which implies that mf_D = f_D. We note also that f_D^M presents significant lower values than mf_D or f_D^P when the fraction of donor in interaction is lower than 0.25. This result is in agreement with our previous results obtained from Monte Carlo simulations and experimental measurements on fluorescent solutions. This behavior is also visible in Fig. 8C3 because f_D^M is non null only when the fraction of interacting donor (mf_D or f_D^P) is greater than 0.2; otherwise the pixel of f_D^M image is black. We have represented in Fig. 8D, the lifetime images of τ_F^P and τ_F^M. The τ_F^P image is well resolved and its distribution is centered around 0.7 ns. Concerning the τ_F^M image, the pixels can be divided into two populations: the pixels in black correspond to f_D^M lower than 0.2 (out of the domain of validity of the moments method) and the others correspond to f_D^M higher than 0.2 and consequently correct fluorescence lifetime values. These results confirm that the combination of our fast-FLIM prototype with direct non-fitting methods (which are easily automated) allows quantifying correctly the spatiotemporal FRET parameters for Rac activation in living cells and more generally for protein-protein interactions.

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Figure 8. Experimental FLIM measurements with our fast-FLIM prototype for quantifying G protein activation in living cells.

The polar plots of a 3T3 cell co-expressing Rac-GFP and PBD-mCherry (with N_mean = 850 photons) and of a cell co-expressing Rac-GFP+mCherry (with N_mean = 830 photons) as a reference (negative control) are shown in (A). The shift between the two spots is the proof of lifetime modification which is also clearly visible in the mean lifetime images <τ> (scale bar: 10 µm). We have plotted in (B) the temporal variations of the mean lifetime for each cell. We have also calculated f_D^P, f_D^M and mf_D of the cell co-expressing Rac-GFP and PBD-mCherry and the images are reported respectively in (C1), (C2) and (C3). The evolution of each parameter calculated in the white region of interest is also plotted in (C4). We finally show the images of τ_F^P and τ_F^M in (D1) and (D2) and the corresponding lifetime distributions in (D3).

https://doi.org/10.1371/journal.pone.0069335.g008