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Abstract
Reliable measurements of calibration parameters are crucial for quantitative three-cube Förster resonance energy transfer (FRET) measurements. Here we have developed a single-cell-based calibration method (SCC-FRET), which can simultaneously obtain spectral crosstalk correction parameters (β and δ) and calibration parameters (G and k) of a quantitative FRET system by imaging a cell expressing one kind of standard FRET plasmid with a known FRET efficiency (E) and the donor-to-acceptor concentration ratio (RC). We performed the SCC-FRET method on a three-cube FRET microscopy for the cells expressing C5V, and obtained β = 0.150 ± 0.000, δ = 0.610 ± 0.000, G = 2.840 ± 0.065, and k = 0.847 ± 0.013. These parameters were used to measure the E and RC values of C17V and C32V constructs in living cells and obtained EC17V = 0.382 ± 0.010 and EC32V = 0.311 ± 0.007, RC17V = 1.010 ± 0.023 and RC32V = 1.050 ± 0.022, consistent with the reported values, demonstrating the effectiveness of the the SCC-FRET method. We also performed the SCC-FRET method for the cells with different S/N levels (S/N > 10, 10 > S/N > 3, 3 > S/N > 1, respectively), and obtained consistent system calibration parameters under different S/N levels, indicating excellent robustness. SCC-FRET requires only imaging a cell expressing one kind of standard FRET plasmid for measuring all calibration parameters under identical imaging conditions, rendering the SCC-FRET method extremely convenient, accurate, and robust. The SCC-FRET provides strong support for expanding the biological application of quantitative FRET analysis in living cells.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Förster resonance energy transfer (FRET) technology has been widely used to map temporal–spatial dynamics of intracellular biochemical events in living cells [1–8]. Three-cube FRET microscopy, a fluorescence intensity-based FRET quantification system, is the most used approach for live-cell FRET quantification imaging [9–12]. Three images are obtained from three channels of three-cube FRET microscopy for FRET imaging: the donor (D) channel image (IDD, which is the fluorescence intensity image of the donor channel with donor excitation), the acceptor (A) channel image (IAA, which is the fluorescence intensity image of the acceptor channel with acceptor excitation), and the FRET channel image (IDA, which is the fluorescence intensity image of the acceptor channel with donor excitation) [13]. Three-cube FRET imaging consists of the three steps [11]: (1) measuring the spectral crosstalk coefficients (a, b, c, and d) between the three channels; (2) determining the sensitized-quenching transition factor (G), and the ratio of donor to acceptor fluorescence intensity at equimolar concentrations when FRET is absent (k) [15]; and (3) capturing IDD, IDA, and IAA images of FRET samples for FRET imaging [11].
Reliable measurements of a, b, c, d, G, and k are crucial for quantitative FRET imaging [9–14]. The spectral crosstalk coefficients a, b, c, and d are the calibration parameters for the fluorescence crosstalk between the donor and acceptor emission spectra. The k factor is a ratio of donor fluorescence intensity to acceptor fluorescence intensity under the conditions of equimolar concentrations when FRET is absent [9]. The G is the FRET sensitized-quenching transition factor that is a ratio of sensitized acceptor emission to quenched (i.e., lost) donor emission [10]. Hoppe et al. determined the G by using a donor-acceptor fusion protein with predetermined FRET efficiency as a reference point [15]. Zal and Gascoigne utilized an acceptor photo bleaching-based approach to determine G [10]. Nagy et al. used three kinds of tandem FRET plasmids with different FRET efficiencies to obtain G [16]. Chen et al. proposed the use of two types of FRET plasmids with unknown FRET efficiencies, from different dish cultures, to obtain G [9]. We used a dish of cells, culturing two kinds of cells expressing different FRET plasmids (with significantly different FRET efficiency) in one dish, to measure G. This improved the stability of G during measurement [13,17].
The inability to simultaneously measure these calibration parameters under identical conditions impedes the widespread application of live-cell quantitative FRET imaging [7]. The a, b, c, and d depend on the emission and excitation spectra of the donor and acceptor, filter set, and spectral response of the camera [18]. Conventionally, imaging an acceptor-only sample measures a and b, and imaging a donor-only sample measures c and d. The parameter G is crucial for the calculation of FRET efficiency because it relates the level of sensitized emission to the drop in donor fluorescence attributable to FRET [10]. As FRET signals appear and are used to reveal intracellular biochemical events, the calibration of G becomes more difficult. Therefore, researchers are attempting to develop better methods to determine G for accurate calibration of FRET systems [9,10,13,15–17]. Once G is determined, k can be determined using a 1:1 donor acceptor [9]. In order to measure a, b, c, d, G, and k, at least three dishes of cells transfected with different plasmids are used, and these calibration parameters are measured with different live cells. Due to differences in samples, and the state and protein expression of live cells, measurement of these calibration parameters is not performed under identical conditions, which can easily cause failure or inaccurate calibration of the FRET system.
Here, we propose a single-cell-based calibration method for FRET systems (SCC-FRET) that can simultaneously determine β, δ, G, and k under identical conditions. The spectral crosstalk correction parameters β = a - bd and δ = d - ac replace the role of the spectral crosstalk coefficients a, b, c, and d in FRET imaging. A cell expresses a standard FRET plasmid with a known FRET efficiency ($E_D^0$) and donor-to-acceptor concentration ratio ($R_C^0$). One region of cell images was selected to collect three-channel fluorescence intensity, and E-FRET theory was used to establish the experimental values ($E_D^1$ and $R_C^1$) containing the unknown calibration parameters (β, δ, G, and k). The calibration parameters of the FRET system were measured by minimizing the residual sum F (β, δ, G, k) of |$E_D^1$ − $E_D^0$| and |$R_C^1$ -$R_C^0$ | under the given parameter constraints. We performed SCC-FRET using a FRET microscope to evaluate its practical performance. The SCC-FRET method can determine β, δ, G, and k using a single cell expressing a standard FRET plasmid, which meets the strict requirements of measurement under uniform conditions. Moreover, β, δ, G, and k are measured simultaneously in a single step, and an optimal set of β, δ, G, and k is automatically obtained, the same way spectral crosstalk and FRET processes occur simultaneously during FRET imaging. SCC-FRET circumvents complex calibration steps and the use of multiple samples, making calibration extremely convenient. The excellent accuracy and robustness of the SCC-FRET method lay the foundation for reliable and rapid FRET quantification in live cells.
2. Methods and materials
2.1 SCC-FRET method
The SCC-FRET method determines the calibration parameters β, δ, G, and k by solving the equations constructed based on the E-FRET imaging theory [10–12], least square optimization theory, and system spectral analysis. The expressions for FRET efficiency (ED) and donor-to-acceptor concentration ratio (RC) in the E-FRET theory are transformed as follows:
Based on the least squares optimization theory, the calibration parameters β, δ, G, and k of the FRET system can be determined by following the SCC-FRET equation:
Constraints (s.t.) are beneficial for quickly solving the SCC-FRET equation and obtaining accurate calibration parameters. In addition, ${\delta _D}$ and ${\beta _A}$ can also be obtained by conventional experiments, such as imaging a donor-only or acceptor-only sample to measure d (replacing ${\delta _D}$) and a (replacing ${\beta _A}$), respectively [10].
For a three-cube FRET system, β, δ, G, and k are measured simultaneously under identical conditions by solving the SCC-FRET equation, which minimizes the residual sum F (β, δ, G, k) of |$E_D^1$ − $E_D^0$| and |$R_C^1$ − $R_C^0$ | under the given parameter constraints. SCC-FRET is performed in multiple fields of view and the measured means are used as the final calibration parameters of the FRET system. FRET measurements of the experimental samples are performed using Eq. (1) and (2), respectively.
2.2 Cell culture, transfection, and plasmids
Hela cells obtained from the Department of Medicine (Jinan University, Guangzhou, China) were cultured just as described previously [14]. Cells were cultured in Dulbecco’s modified Eagle’s medium (DMEM, Gibco, Grand Island, New York) containing 10% fetal calf serum (Sijiqing, Hangzhou, China) at 37°C under 5% CO2 in a humidified incubator.
For plasmids, Cerulean (C, a blue fluorescent protein variant serving as the donor) and Venus (V, a yellow variant serving as the acceptor) plasmids were purchased from Addgene Company (Cambridge, Massachusetts, USA). The Vogel laboratory (National Institutes of Health, Bethesda, Maryland) kindly provided C32V (Cerulean-32-Venus), C17V (Cerulean-17-Venus), and C5V(Cerulean-5-Venus).
For transfection, cells were cultured in DMEM containing 10% fetal calf serum in a 30-mm glass dish at 37°C under 5% CO2 in a humidified incubator. After 24 h, when the cells reached 70% to 90% confluence, plasmid was transfected into the Hela cells for 24-48 h by using Lipofectamine 2000 (Invitrogen, Carlsbad, American) in vitro transfection reagent.
2.3 Living-cell fluorescence imaging
Imaging was performed on a Zeiss ApoTome.2 image system (Axio Observer 7, Carl Zeiss, Oberkochen, Germany) equipped with an inverted widefield fluorescence microscope, an ApoTome.2 modules for structured illumination, and a CCD camera (Axiocam 506 mono, Carl Zeiss, Oberkochen, Germany) for imaging. The widefield fluorescence microscope consists of a metal halide lamp (X-Cite 120, 120Q, Excelitas, Massachusetts, USA), a 63×1.4 NA oil immersion, and three filter-cubes. Each Cube is composed of an excitation filter, a dichroic filter, and an emission filter. Cube-1 comprising a BP436/20 excitation filter, a dichroic mirror of DFT 455 and a BP480/40 emission filter was used to obtained IDD images; Cube-2 comprising a BP500/20 excitation filter, a dichroic mirror of DFT 515 and a BP535/30 emission filter was used to obtained IAA images; Cube-3 comprising a BP436/20 excitation filter, a dichroic mirror of DFT 455 and a BP535/30 emission filter was used to obtained IDA images.
3. Results and discussion
3.1 SCC-FRET equation of FRET system
To determine the SCC-FRET equation for our FRET system, we obtained ${\delta _D}$ and ${\beta _A}$ using Eq. (4). Using fluorescent protein databases [19], we can easily obtain ${\beta _A}$ and ${\delta _D}$. The spectra of Cerulean, Venus, and filters were displayed using FPbase (Fig. 1). As shown in Fig. 1(a), Filter 480/40bp, Filter 535/30bp, Cerulean EM, and Cerulean EX are the donor emission filter spectrum, acceptor emission filter spectrum, donor emission spectrum, and donor excitation spectrum, respectively. $e_{{D^{em}}D_{\textrm{filter}}^{em}}^{max}$ was 1.000, and the $e_{{D^{em}}A_{\textrm{filter}}^{em}}^{max}$ was 0.611. As shown in Fig. 1(b), Filter 436/20bp, Filter 500/20bp, Venus EM, and Venus EX are the donor excitation filter spectrum, acceptor excitation filter spectrum, acceptor emission spectrum, and acceptor excitation spectrum, respectively.$e_{{A^{ex}}A_{\textrm{filter}}^{ex}}^{max}$ was 0.902, and $e_{{A^{ex}}D_{\textrm{filter}}^{ex}}^{max}$ was 0.054. The relative intensity ratio, $\phi $, of the light source X-Cite120Q at the central wavelengths of the donor excitation filter (446 nm) and the acceptor excitation filter (510 nm) was approximately 2.500. Substituting these values into Eq. (4) yielded ${\delta _D}$ and ${\beta _A}$ values of 0.611 and 0.150, respectively. By substituting ${\delta _D}$ and ${\beta _A}$ into Eq. (3), we derived the SCC-FRET equation [Eq. (5)] for the FRET system. For Eq. (5), $E_D^0$ and $R_C^0$ are the known FRET efficiency and donor-to-acceptor concentration ratio of a standard FRET pair used for calibration, and the system calibration parameters β, δ, G, and k are unknown.
Fig. 1. ${\delta _D}$ and ${\beta _A}$ of the FRET system. The spectra of (a) and (b) were displayed using FPbase, a community-editable fluorescent protein database [19]. (a) Filter 480/40 bp, Filter 535/30 bp, Cerulean EM, and Cerulean EX are the donor emission filter spectrum, acceptor emission filter spectrum, donor emission spectrum, and donor excitation spectrum, respectively. ${\delta _D}$ is the ratio of $e_{{D^{em}}A_{\textrm{filter}}^{em}}^{max}$ (0.611) to $e_{{D^{em}}D_{\textrm{filter}}^{em}}^{max}$(1.000); thus, ${\delta _D}$ = 0.611. (b) Filter 436/20 bp, Filter 500/20 bp, Venus EM, and Venus EX are the donor excitation filter spectrum, acceptor excitation filter spectrum, acceptor emission spectrum, and acceptor excitation spectrum, respectively. ${\beta _A}$ is the product of $\phi $ (2.500) and the ratio of $e_{{A^{ex}}D_{\textrm{filter}}^{ex}}^{max}$ (0.054) to $e_{{A^{ex}}A_{\textrm{filter}}^{ex}}^{max}$ (0.902); thus, ${\beta _A}$ = 0.150.
Fig. 2. Spectral crosstalk coefficients a, b, c, and d. (a) The IDD, IDA, and IAA of the cells expressing Venus (acceptor), and the corresponding pseudo-color images and histograms of the coefficients of a and b. (b) The IDD, IDA, and IAA of the cells expressing Cerulean (donor), and the corresponding pseudo-color images and histograms of the coefficients of c and d.
3.2 Measuring the calibration parameters using SCC-FRET
We performed SCC-FRET on a single cell and field of view with multiple cells. Figure 3(a) shows the representative ${I_{DD}}$, ${I_{DA}}$ and ${I_{AA}}$ images of cells expressing C5V ($E_D^0 = 0.43,R_C^0 = 1.00$) and ten regions of interest (ROIs) in a single cell. We solved Eq. (5) using MATLAB (2019a) and obtained measurements of β, δ, G, and k for the ten ROIs.
Fig. 3. Performing SCC-FRET on a field of view with multiple cells. (a) The representative ${I_{DD}}$, ${I_{DA}}$ and ${I_{AA}}$ images of cells expressing C5V, and ten ROIs of a single cell. Scale bar, 20 µm. (b)-(i) The corresponding histograms of β, δ, G, and k measured by SCC-FRET method and the corresponding pseudo-color images of β, δ, G, and k. (j) The corresponding mean ± SD of β, δ, G, and k.
The calibration parameters β, δ, G, and k of the FRET system can be quickly measured by the SCC-FRET method, requiring only one ROI of a single cell, and achieving good consistency for multiple measurements on a single cell. The three-channel fluorescence intensities of the ten ROIs (with background correction) and the corresponding β, δ, G, and k measurements are listed in Table 1. The mean ± standard deviation (SD) of β, δ, G, and k are 0.150 ± 0.000, 0.610 ± 0.000, 2.688 ± 0.035, and 0.822 ± 0.006, respectively. The time taken for a single measurement on a personal computer (windows 10, AMD-R5-3600 processor) is approximately 0.2 seconds.
Table 1. SCC-FRET was performed on ten ROIs of a single cell in Fig. 3(a).
Furthermore, we performed SCC-FRET in this field of view [Fig. 3(a)] and observed that the β and δ values measured from different cells were consistent. In our code, 10 × 10 pixels were taken as the ROI, the three-channel fluorescence intensities of ROIs from all cells were extracted, and all ROIs were measured using Eq. (5). The field of view contained 238 ROIs, all of which were obtained using the SCC-FRET method. We obtained 238 sets of calibration parameters from this field of view. The corresponding frequency histograms for β, δ, G, and k are shown in Fig. 3(b), 3(c), 3(d), and 3(e), respectively. The corresponding measurements of ROIs are displayed on the corresponding pixels of the pseudo-color images [Fig. 3(f), 3(g), 3(h), and 3(i)]. As shown in Fig. 3(j), the mean ± SD of β, δ, G, and k are 0.150 ± 0.000, 0.610 ± 0.000, 2.753 ± 0.268, and 0.805 ± 0.067, respectively. As shown in the corresponding histograms [Figs. 3(b) and 3(c)] and pseudo-color images [Figs. 3(f) and 3(g)], the β and δ values measured from different cells are consistent. This can be attributed to the spectral crosstalk parameters β and δ being physical quantities independent of the FRET signals and remain unaffected by the live cell state and protein expression.
As shown in the corresponding histograms [Fig. 3(d) and Fig. 3(e)] and pseudo-color images [Fig. 3(h) and Fig. 3(i)], we observed small differences in G and k measured for different cells. This is because G and the determination of k are closely related to FRET signals, in which energy is transferred nonradiatively (i.e., via long-range dipole-dipole coupling) from a fluorophore in an electronic excited state serving as a donor, to another chromophore or acceptor [1]. This process is influenced to some extent by the live cell state and protein expression, leading to G and k differing slightly for different cells. SCC-FRET avoids the error caused by sample switching and multiple step-by-step calculations, and automatically approximates the true calibration parameters by minimizing F. These experimental results demonstrate that SCC-FRET not only circumvents the use of multiple samples but also determines β, δ, G, and k simultaneously under identical conditions, exhibiting excellent convenience, accuracy, and robustness.
3.3 SCC-FRET under different signal-to-noise ratios
To further test the stability of SCC-FRET, we performed SCC-FRET under different signal-to-noise ratios (S/N). S/N is the ratio of the mean fluorescence intensity of the three channels of an ROI of cells to an ROI of the background. Figure 4(a) shows representative ${I_{DD}}$, ${I_{DA}}$ and ${I_{AA}}$ images of cells expressing C5V, including cells with different S/N values. We divided S/N into three levels: high S/N (S/N > 10), medium S/N (10 > S/N > 3), and low S/N (3 > S/N > 1). Three kinds of cells with different S/N levels were marked in Fig. 4(a). We performed SCC-FRET method in these cells [Fig. 4(b)]. Twenty measurements were performed on each cell, and the mean ± SD histograms are shown in Fig. 4(b). The data measured at different S/N levels are shown in Table 2. As shown in Fig. 4(b), the SCC-FRET method exhibited excellent stability at low S/N ratios. This experiment indicates that SCC-FRET can accurately measure calibration parameters with high robustness at low S/N values.
Fig. 4. SCC-FRET under different signal-to-noise ratios (S/N). (a) The representative ${I_{DD}}$, ${I_{DA}}$ and ${I_{AA}}$ images of cells expressing C5V and three cells with different levels of S/N were marked. Scale bar, 20 µm. (b) The corresponding mean ± SD histograms of β, δ, G, and k under three different levels of S/N.
Table 2. Measurement results of SCC-FRET performed on three cells with different S/N in Fig. 4(a).
3.4 Calibration using the SCC-FRET method and validation using FRET imaging
We implemented the SCC-FRET method using live cells expressing the C5V plasmid for calibration, and FRET imaging using live cells expressing the C17V and C32V plasmids for validation. Figure 5 shows the representative ${I_{DD}}$, ${I_{DA}}$ and ${I_{AA}}$ images of cells expressing the standard FRET plasmids (C17V and C32V) and the corresponding ${E_D}$ and ${R_C}$ images measured by Eqs. (1) and (2). The ${E_D}$ and ${R_C}$ values were measured using the mean values of β, δ, G, and k. The SCC-FRET was performed on 20 fields of view, and the mean values of β, δ, G, and k were taken as the final system calibration parameters. The measurement was repeated 30 times, and the results are presented in Fig. 6(a) and Table 3. Similarly, FRET imaging was performed on 20 fields of view and the mean values were taken as the final ${E_D}$ and ${R_C}$. The FRET imaging was repeated 30 times, and the ${E_D}$ and ${R_C}$ values are shown in Fig. 6(b) and Table 3. The experiments showed that the ${E_D}$ and ${R_C}$ values measured are consistent with those reported in literature [9,13,14], indicating the accurate system calibration with SCC-FRET.
Fig. 5. The representative images of cells expressing the standard plasmids and the corresponding ${E_D}$ and ${R_C}$ images measured by the Eqs. (1) and (2). The representative ${I_{DD}}$, ${I_{DA}}$ and ${I_{AA}}$ images of cells expressing standard plasmids C17V and C32V, the corresponding pixel-to-pixel pseudo-color images of the ${E_D}$ and ${R_C}$, and the corresponding histograms of the ${E_D}$ and ${R_C}$. Scale bar, 20 µm.
Fig. 6. The system calibration parameters measured by SCC-FRET and ED and RC values for cells expressing standard plasmids (C17V and C32V) measured by FRET imaging.
Table 3. Calibration using the SCC-FRET method and validation using FRET imaging.
4. Conclusion
We developed the SCC-FRET method, which is a single-cell-based calibration method for three-cube FRET systems. The excellence of the SCC-FRET method is the ability to simultaneously measure β, δ, G, and k under identical conditions. In addition to greatly reducing the preparation of experimental samples and imaging of multiple samples, SCC-FRET determines the calibration parameters in one step, thereby significantly reducing errors from multiple steps and manual interventions in the calibration process. Experiments proved that SCC-FRET can achieve system calibration with excellent convenience, robustness, and accuracy. The SCC-FRET method can effectively calibrate the commonly used three-cube FRET systems, which is beneficial for expanding the biological applications of FRET quantitative analysis in living cells.
Funding
National Natural Science Foundation of China (61875056, 62135003); Science and Technology Program of Guangzhou (2019050001).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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