1.

Introduction

The role of mechanotransduction in biology has been extensively reviewed and points to a significant and central role played by mechanical forces and the cytoskeleton in shaping cellular function and behavior.^1–4 The potential to control complex cellular function by understanding mechanotransduction has important implications for the design of therapeutic strategies in many pathological conditions, including degenerative diseases and injury, cancer, and aging.

While the subcellular localization of adhesion molecules and the architecture of focal adhesions can be imaged by conventional and by super-resolution fluorescence microscopy,^5,6 actual tension measurements require techniques that are sensitive to piconewton level forces at the cellular and subcellular scales. To this end, fluorescence resonance energy transfer (FRET) probes consisting of molecular springs inserted between a fluorescent donor and acceptor pair have been the focus of much recent interest. Changes in molecular tension are measured by quantifying changes in the FRET signal between the donor and acceptor.^7–9 Intramolecular tension-sensing fluorescent probes have been demonstrated,^10,11 where an elastic linker module flanked by an FRET donor and acceptor pair is inserted into a load-bearing protein using recombinant DNA methods. Unlike FRET biosensors that toggle between a high and low FRET state, these FRET tension probes are expected to report on a nonbinary, spatiotemporal intracellular distribution of mechanical load. Thus, the ability to quantify accurately their FRET efficiency presents a challenge for microscopic imaging.

A sensitive and direct method to measure changes in FRET signal relies on measuring the donor’s fluorescence lifetime in the presence of the acceptor (${\tau }_{\mathrm{DA}}$), relative to the donor’s lifetime in the absence of the acceptor (${\tau }_D$).¹² Thus, FRET imaging can be achieved via fluorescence lifetime imaging microscopy (FLIM), using only measurements within the donor’s spectral emission channel. Fluorescence lifetime is largely independent of fluorophore concentration, and with selection of appropriate spectral filters, the donor channel can be made free of cross-talk signal from the acceptor. Using this FLIM-FRET approach, fluorescent donors can even be coupled with nonfluorescent acceptors, expanding the range of viable donor-quencher pairs. However, the donor and acceptor fluorophores in FRET sensors are typically separated by a flexible linker, giving rise to fluorescence emission decays with multiple time constants. Thus, FLIM systems designed to measure FRET typically rely on resolving multiexponential decays and then calculating FRET efficiency from the amplitude-weighted average lifetime.¹²

Two approaches to FLIM may be implemented for FRET applications. Time-domain (TD) FLIM consists of measuring the fluorescence signal decay as a function of time after exciting the sample with a very short laser pulse. On the other hand, frequency-domain (FD) FLIM consists of measuring fluorescence lifetime by measuring the modulation and phase of the fluorescence emission excited by a frequency-modulated laser source. Both of these approaches have been extensively reviewed in the literature and are utilized in numerous applications ranging from metabolic imaging to protein conformation and protein interaction.^12–15 Recent developments in FLIM technology have also given rise to approaches for achieving high speed depth-resolved,^16–19 widefield,^20–23 and multichannel²⁴ FLIM. For example, Bower et al. recently demonstrated a state-of-the-art high-speed FLIM system using a mode-locked pulsed Ti:Sapphire laser synchronized with a 1.8-GS/s digitizer to directly sample the fluorescence decay signal and analyze it by a single exponential fit, with temporal resolution only limited by the sampling rate of the digitizer.¹⁶ Commercially available FLIM systems include highly sensitive frequency-domain fluorescence lifetime imaging microscope (FD-FLIM) systems (for example, ISS Inc, Lambert Instruments BV) operating at multiple modulation frequencies or phases, as well as TD-FLIM systems that rely on time-correlated single photon counting (for example, Becker and Hickl GmbH, Picoquant GmbH, Leica Microsystems, Inc). These highly sensitive systems are capable of accurately measuring multiexponential lifetimes, which are expected for FRET probes within living cells such as the tension probe investigated here. In addition, FD-FLIM systems operating at multiple modulation frequencies allow for approaches such as the polar, or phasor, plots for analysis of complex multiexponential lifetimes.^19,25 However, current barriers to adopting FLIM to quantify FRET efficiency still exist due to the high cost of pulsed laser sources, the potential complexity of data acquisition and analysis, and the relatively slow imaging speed of FLIM in weakly fluorescent samples, requiring long integration times to accurately resolve multiexponential decays. The use of femtosecond-pulsed laser sources combined with multi-GHz digitizers and the need for multiple excitation and emission channels also result in a multiplicative growth of system cost and complexity.

In this paper, we implement a simplified FD-FLIM imaging system for FRET applications. The system is based on the instrument described by Booth and Wilson.²⁶ The system relies on measuring, at a single modulation frequency, the apparent lifetime of a fluorophore and its corresponding apparent FRET efficiency. Instead of resolving and measuring multiple exponential decays, we use a FRET standards calibration curve to convert the measured apparent FRET efficiency to true FRET efficiency. This approach allows us to utilize sinusoidally modulated laser diodes at single modulation frequencies for fluorescence excitation, and signal processing techniques based on the discrete Fourier transform to implement FD-FLIM in a cost-effective, modular format, which has several advantages. Laser diodes are available at many excitation wavelengths relevant for many fluorescence samples, and they are relatively inexpensive compared with the pulsed laser sources utilized in commercial FLIM systems. Many diodes can be directly intensity modulated at tens to hundreds of MHz using a bias-T modulation circuit by a voltage signal generated by an arbitrary waveform generator. The Fourier transform used for signal processing can achieve phase measurements with much higher accuracy than the $2\pi$ time period of a modulated signal. Thus, subnanosecond time resolution can be obtained when modulating a laser in the 20- to 50-MHz range. To generate and measure signals in this frequency range, the Nyquist sampling theory allows the use of electronics with bandwidth on the order of 50 MHz and data converters and sampling rate on the order of 100 MHz. This significantly reduces the cost of the data acquisition hardware compared to the electronics operating in the GHz range in current state-of-the-art high speed FLIM systems. Digitizers are used to measure directly the photon current of highly sensitive PMTs and avoid the photon “pile-up” problem, which may arise when multiple photons arrive at the same time while detecting fluorescence signals with PMTs operating in the single photon-counting regime. This in turn helps improve total optical throughput and the measurement dynamic range of the system. Finally, the fluorescence emission signal may be split spectrally by optical filters toward different detectors, each acting as an analog input channel. The Fourier transform applied to these multiple input channels allows phase measurements at all modulation frequencies (and therefore excitation wavelengths) simultaneously, and the processes are identical on different emission wavelength channels.

We evaluate the system’s performance by measuring the apparent lifetime of mTFP1 in mTFP1-mVenus constructs with known high and low FRET efficiency. We show that the FRET efficiency ($E_{\mathrm{FRET}}^{\mathrm{app}}$) estimated based on the apparent lifetime can be related by a linear fit to the known true $E_{\mathrm{FRET}}$ of the constructs. This relationship is then used as a standard-based $E_{\mathrm{FRET}}$ calibration curve to convert an unknown sample’s apparent FRET efficiency measured with our system to its true FRET efficiency. Utilizing this method, we further demonstrate measurements of FRET efficiency in the vinculin tension probe, VinTS¹⁰ at focal adhesions. The use of a single modulation frequency along with the known standards for $E_{\mathrm{FRET}}$ calibration allows us to utilize the apparent lifetime measured at a single modulation frequency to infer FRET efficiency and circumvent the need for using multiple modulation frequencies or measuring multiple exponential decays. This approach provides a cost-effective, fast imaging system that can facilitate FLIM in fields, including mechanobiology, which already involve the preparation of FRET constructs similar to the FRET standards needed for our calibration. While current FLIM systems are capable of providing robust platforms for FRET efficiency measurements, a cost-effective, modular, table-top system would also facilitate FLIM applications such as FRET biosensor development in laboratory settings with limited microscopy resources.

2.

Methods

2.1.

Optical Setup

The schematic of the FD fluorescence lifetime imaging system optimized for measurement of FRET between mTFP1 and mVenus is shown in Fig. 1(a). A 450-nm laser diode (LD1) and a 520-nm laser diode (LD2) are used as the excitation light sources. Two pinhole apertures (PH1 and PH2) of $300\mu \mathrm{m}$ diameter are placed in front of each laser diode as simple spatial light modulators to transform the elliptically shaped laser diode output into circular beams. Lenses L1 and L2 are used for collimation, generating two beams each with a diameter of about 5 mm. These collimated beams are combined by a dichroic filter (DM1) into a common beam path and are directed toward an optical scan-head consisting of XY galvanometer scanners mounted near the back aperture of an objective lens (OBJ). Two objective lenses were used for this study: a Nikon $0.85\mathrm{NA}/60\times$ dry objective and a Nikon $1.3\mathrm{NA}/60\times$ oil immersion objective. The optical power at the sample did not exceed $25\mu \mathrm{W}$ within the scanned point. A multiedge excitation filter (DM2) transmits the two excitation wavelengths and reflects the fluorescent emissions toward a $10\text{-}\mu \mathrm{m}$ confocal pinhole (PH3). Another dichroic filter (DM3) separates the fluorescent emissions into two wavelength bands, subsequently filtered by two emission filters (EM1 and EM2) placed before two photomultiplier tube detectors (PMT1 and PMT2). The excitation and emission spectra of mTFP1 and mVenus along with the filter transmission curves are shown in Fig. S1 in the Supplementary Material.

Fig. 1

(a) Optical setup, (b) generation of modulation waveforms and data synchronization signal with minimum phase jitter. LD1, PL450B (Thorlabs); LD2, L520P50 (Thorlabs); PH1, P300D (Thorlabs); PH2, P300D (Thorlabs); L1, AC127-030-A (Thorlabs); L2, AC080-020-A (Thorlabs); S1,S2, SM1SH1 (Thorlabs); DM1, MD480 (Thorlabs); NDF, ND20A (Thorlabs); DM2, Di01-T457/514/647 (Semrock); XY GALVO, GVS202 (Thorlabs); OBJ, 60X/0.85 plan fluorite objective (Nikon) or 60X/1.30 oil objective (Nikon); L3, AC080-016-A (Thorlabs); PH3, P5D (Thorlabs); L4, AC080-016-A (Thorlabs); DM3, DMLP505 (Thorlabs); EM1, MF479-40 (Thorlabs); EM2, MF559-34 (Thorlabs); PMT1,PMT2, PMT2101 (Thorlabs).

2.4.

FRET Constructs

The FRET constructs used here are summarized in Fig. 2. The $\mathrm{mTFP}1\text{-}{(\mathrm{GGSGGS})}_2\text{-}\mathrm{mVenus}$ and mTFP1-TRAF-mVenus constructs have been described previously in Ref. 31. VinTS and TSMod (Plasmids 26019 and 26021, respectively) were obtained from Addgene. We also used the fluorescent protein monomers mTFP1 and mVenus to obtain the unquenched donor lifetime and to assess detection channel cross talk, respectively. TRAF, GGS, and TSMod are referred to as “soluble constructs” in this paper as they are expected to freely diffuse through the cytosol.

Fig. 2

FRET constructs with expected FRET efficiency based on the values reported by Gates et al.³¹

3.

Results

3.1.

Lifetime Measurements in Control Constructs

The measured lifetimes and calculated $E_{\mathrm{FRET}}^{\mathrm{app}}$ of our fluorescent proteins (mTFP1 and Venus) and our FRET control constructs [$\mathrm{mTFP}1\text{-}{(\mathrm{GGSGGS})}_2\text{-}\mathrm{mVenus}$ and mTFP1-TRAF-mVenus] are shown in Fig. 3. Fluorescence intensity images for each construct are provided for the donor [Figs. 3(a)–3(d)] and acceptor [Figs. 3(e)–3(h)] channels collected with 20 to $25\mu \mathrm{W}$ at the sample. For donor-only cells (mTFP1) and acceptor-only cells (mVenus), the fluorescence is isolated to the donor channel and accepter channel, respectively. Importantly, the cross-talk for mVenus to the donor channel is negligible and cannot be distinguished from background noise, indicating that the lifetime measured in the donor channel can be attributed only to donor emission. Fluorescence from cells with the FRET control constructs appears in both the donor and acceptor channels, confirming that both proteins are present in cells after transfection. The corresponding fluorescence lifetime images [Figs. 3(i)–3(l)] are presented for mTFP1 and the FRET control constructs from the donor channel, whereas the mVenus lifetime image is from the acceptor channel.

Fig. 3

Representative images of cells with the fluorescent proteins (mVenus and mTFP1) and FRET control constructs [mTFP1-TRAF-mVenus and $\mathrm{mTFP}1\text{-}{(\mathrm{GGSGGS})}_2\text{-}\mathrm{mVenus}$]. (a)–(d) Fluorescence intensity in donor channel (450 nm excitation/479 nm emission band modulated at $f_1$). (e)–(h) Fluorescence intensity in acceptor channel (520 nm excitation/559 nm emission band modulated at $f_2$). (i)–(l) Corresponding (i) mVenus and (j)–(l) mTFP1 fluorescence lifetime images. (m) Box and whisker plot for lifetime (left axis) and “apparent” FRET efficiency (right axis). FRET efficiency only applies to samples containing the mTFP1 donor. (n) Normalized histogram of all pixels used to calculate lifetime. All images are captured with $2048\times 2048$ points using the Nikon 0.85 NA $60\times$ objective and a $6.8\text{-}\mu \mathrm{s}$ pixel dwell time.

A blue-to-red color look-up-table is applied to lifetime values for visualization. From this, it is immediately clear that each construct can be distinguished, qualitatively, from the others based on color differences. For quantitative analysis, cells were manually segmented and an intensity-weighted average lifetime was calculated for 145 segmented cells that had a mean relative intensity $>0.01$. Average lifetime values are 3.071 for mVenus ($n=40\text{cells}$), 2.845 for mTFP1 ($n=49\text{cells}$), 2.549 for TRAF ($n=33\text{cells}$), and 1.515 for ${(\mathrm{GGSGGS})}_2$ ($n=23$ cells). These data are displayed in the box and whisker plot in Fig. 3(m) indicating the median (red lines), 25th to 75th percentile (blue boxes), and minimum/maximum (black whiskers) for $n$ number of measured cells. For samples containing the donor, the apparent lifetime was converted to an estimate of FRET efficiency (an apparent FRET) using Eq. (12), which is displayed on the right-hand $y$ axis of Fig. 3(m). While the Venus lifetime is not used to measure the apparent FRET efficiency of the FRET constructs, we include this measurement in Fig. 3(m) to demonstrate the systems’ ability to collect lifetime data from two different fluorophores. Figure 3(n) provides a histogram that includes all pixels used to calculate the average lifetime for each cell. The wider distributions of ${(\mathrm{GGSGGS})}_2$ and TRAF can be attributed to (1) noisier measurements due to weaker signal intensity than cells with mTFP1 or mVenus and (2) the design of the constructs that inherently results in a distribution of FRET efficiency values.

Cells expressing the fluorescent proteins and FRET control constructs were also imaged over a period of time at a high frame rate ($128\times 128$ points with a $6.8\text{-}\mu \mathrm{s}$ pixel dwell time for $\sim 9\mathrm{fps}$). The lifetime of each construct can be accurately determined at this high frame rate as shown in Fig. 4, where the mean lifetime of cells with each construct is 3.165 ns for mVenus, 2.779 ns for mTFP1, 2.354 ns for TRAF, and 1.551 ns for ${(\mathrm{GGSGGS})}_2$. These lifetimes are in agreement with the high pixel density data from Fig. 3, being within the limits of cell-to-cell lifetime variation.

Fig. 4

High-speed imaging and photostability measurements with $25\mu \mathrm{W}$ at the sample (Nikon 0.85 NA $60\times$ objective). (a)–(d) Representative intensity images for cells with the fluorescent proteins and control constructs. (e)–(h) Corresponding fluorescence lifetime images. (i) Plots of intensity over time and (j) lifetime over time for a region of interest within a cell. All images are captured with $128\times 128$ points at $\sim 9\mathrm{fps}$ ($6.8\text{-}\mu \mathrm{s}$ pixel dwell time). mVenus in (a) is excited with 520 nm and detected within the emission band centered at 559 nm, whereas mTFP, TRAF, and ${(\mathrm{GGSGGS})}_2$ are excited with 450 nm and detected within the emission band centered at 479 nm.

The mean intensity and lifetime were measured for a region of interest within a single cell to ensure that photobleaching was minimal. Figure 4 shows the stability of the lifetime data over a period of 120 s (535 frames) when capturing high frame rate images ($128\times 128\text{pixels}$). The lifetime of all the samples remained within 2.9% of the initial values after 120 s. For the Nikon 0.85 NA $60\times$ objective and the 450-nm laser diode, the fluence for a single pixel in the $128\times 128$ image is estimated for the diffraction-limited spot with a $6.8\text{-}\mu \mathrm{s}$ pixel dwell time and is equal to $0.052\mathrm{J}/{\mathrm{cm}}^2$. Over the 120-s measurement, each image pixel is scanned 535 times for a total fluence of $535\times 0.052\mathrm{J}/{\mathrm{cm}}^2=27.8\mathrm{J}/{\mathrm{cm}}^2$. The imaging protocol used for data in this report consisted of locating and focusing on cells for no more than 60 s before capturing a high pixel density image, ensuring that images were captured in the regime where photobleaching effects on lifetime measurements are minimal.

3.2.

Lifetime Measurement in the Vinculin Tension Sensor (VinTS)

To investigate the capabilities of the imaging system in the case of weakly emitting samples that require high-resolution imaging, VinTS was overexpressed in our iBMK cells and its lifetime was compared with that of the unloaded tension module, TSMod. VinTS consists of the elastic tension module TSMod inserted between the head and tail of vinculin.¹⁰ Previous work has demonstrated that VinTS localizes to focal adhesions, similar to vinculin, and bears load at these structures.¹⁰ The expression levels of VinTS in our iBMK cells were significantly lower than those of the soluble constructs. The fluorescence intensity of VinTS was typically an order of magnitude lower than the signal of the soluble FRET constructs including TSMod [see colorbar in Figs. 5(a) and 5(e)]. Focal adhesions are structures on the order of a few microns and require a high resolution objective in order to be properly resolved. For these studies, a Nikon 1.3 NA $40\times$ oil immersion objective was used. $1024\times 1024$ pixel images were acquired by scanning over a field of view of width $190\mu \mathrm{m}$. The pixel dwell time was $27.2\mu \mathrm{s}$ resulting in $\sim 28\mathrm{s}$ per frame.

Fig. 5

Comparison of TSMod and VinTS showing cropped regions of $1024\times 1024$ images (Nikon 1.3 NA $40\times$ objective, $27.2\mu \mathrm{s}$ pixel dwell time). (a), (e) Representative images of the fluorescence intensity. (b), (f) Corresponding fluorescence lifetime images. (c), (g) pixel masks used for selecting the cells for TSMod and adhesions for VinTS. (d), (h) Processed images after applying the mask and $2\times 2$ intensity-weighted pixel binning. (i) Box and whisker plot for lifetime (left axis) and “apparent” FRET efficiency (right axis). The asterisks denote a significant difference between the mean lifetimes of VinTS and TSMod ($p<{10}^{-6}$ by Student’s $t$-test).

Figure 5 presents example images for TSMod and VinTS samples captured in the donor channel. Cropped regions of the acquired fluorescence intensity images are shown in Figs. 5(a) and 5(e) with their corresponding lifetime images in Figs. 5(b) and 5(f). Processing steps were taken to create pixel masks [Figs. 5(c) and 5(g)] that section only the cells for TSMod samples and only adhesions for VinTS samples. Since fluorescence intensity was weak for VinTS, $2\times 2$ intensity-weighted pixel binning was applied to all VinTS and TSMod lifetime images as a means to generate a more accurate lifetime measurement per pixel (see Sec. 2.6). The final processed images in Figs. 5(d) and 5(h) were used to calculate the mean lifetime for VinTS and TSMod in cells. The mean intensity-weighted lifetime was calculated for all VinTS ($n=94$ adhesions) and TSMod ($n=50\text{cells}$) samples with a mean relative intensity $>0.01$. These results are presented in Fig. 5(i), where the mean VinTS lifetime at the adhesion points was $2.30\pm 0.16\mathrm{ns}$, which is significantly ($p<{10}^{-6}$ by Student’s $t$-test) longer than that of the (unloaded) TSMod ($2.02\pm 0.16\mathrm{ns}$). The conversion to apparent FRET efficiency is displayed on the right-hand axis of Fig. 5(i).

3.3.

Comparison Between Apparent E_FRET Based on FLIM and True E_FRET

Given the fact that we expect to probe an ensemble of molecules corresponding to a given FRET construct and possessing a distribution of lifetimes,³³ our phase measurement conducted at a single modulation frequency corresponds to an apparent lifetime measurement, which depends on the modulation frequency that we choose. To address this, we plotted, in Fig. 6, the estimated $E_{\mathrm{FRET}}^{\mathrm{app}}$ obtained from the measured apparent lifetimes [Eq. (12)] of the soluble FRET constructs, against the published values of $E_{\text{FRET}}$ measured independently by the sensitized emission method.³¹ The published values for these constructs are $E_{\mathrm{GGS}}=0.483$, $E_{\mathrm{TRAF}}=0.053$, and $E_{\mathrm{TSMod}}=0.286$.³¹ We also included a zero-FRET point to account for the donor-only case. The plot demonstrates a linear relationship between the measured FRET efficiency based on the single modulation phase and the true $E_{\mathrm{FRET}}$ of the constructs measured independently using a sensitized emission-based method.³⁴ Two linear fits, with and without an intercept, are shown in Fig. 6 and suggest that the $E_{\mathrm{FRET}}^{\mathrm{app}}$ measured by FLIM is within 2% to 8% of the $E_{\text{FRET}}$ measured by the sensitized emission method for the soluble FRET control constructs. This linear relationship, which is obtained at a given modulation frequency, may be utilized as a sample-based calibration to correct for the discrepancy between the $E_{\mathrm{FRET}}^{\mathrm{app}}$ value obtained from the apparent lifetime measurement and the true FRET efficiency. For example, we can convert the average apparent $E_{\mathrm{FRET}}^{\mathrm{app}}$ of VinTS (19.28%) to its expected value given the slope of the line in Fig. 6. This results in an average $E_{\text{FRET}}$ of 18.07% (line with intercept) or 19.49% (line without intercept) for VinTS.

Fig. 6

Relationship between the $E_{\mathrm{FRET}}^{\mathrm{app}}$ calculated from the apparent lifetime measured at a single modulation frequency (42.1875 MHz) and published $E_{\text{FRET}}$ measured independently by the sensitized emission method. A line was fit to the data points corresponding to the soluble FRET constructs (GGS, TRAF, and TSMod), and the point at (0,0) corresponding to zero FRET efficiency (donor only). The points corresponding to VinTS were obtained by finding the true $E_{\text{FRET}}$ for VinTS based on the slope obtained from the corresponding linear fits. Data points are mean ± standard deviation, with $n=23$ (GGS), $n=33$ (TRAF), $n=50$ (TSMod), and $n=94$ (VinTS).

4.

Discussion

We have developed a two-channel FD FLIM system based on single modulation frequencies for each excitation wavelength. In this setup, the modulation waveform is a simple sinusoidal function and is fully defined by a digital waveform stored in a memory map (WFM1 MEM MAP). Other functions with harmonic frequencies may also be utilized. The system requires knowledge of the instrument-induced phase delay, which may be measured using solutions of calibration standards, such as coumarin-6 and fluorescein, with known single exponential lifetimes. The system introduced phase shift may arise from several sources including the capacitor charging time in the laser diode junction and the bias-T modulation circuit, electric and optical cable propagation delay, and phase shift in the amplifiers of the detector and digitizer circuits. In practice, this system-introduced phase shift is a constant unless the system configuration is changed, such as by changing cable length or introducing a free-space optical delay in the signal path.

To evaluate the performance of our system, we measured the apparent lifetime of mTFP1 in mTFP1-mVenus FRET standards expressed in living cells to demonstrate our ability to differentiate the short and long lifetime of mTFP1 corresponding to the FRET standards with short ${(\mathrm{GGSGGS})}_2$ or long (TRAF) linker, respectively (Fig. 3). These measurements are based on previous work in which such FRET standards were utilized to evaluate FLIM systems.^29,35–37 In addition, we show that the lifetime of VinTS at focal adhesions is significantly ($p<{10}^{-6}$) longer than the lifetime of the unloaded TSMod probe (Fig. 5). Even under static culture conditions, cells generate large forces without being actively perturbed. Under these conditions, the vinculin tension sensor reports on the loads vinculin experiences within focal adhesions due to the force-generation capabilities of the actomyosin cytoskeleton.^10,38,39 Fluctuations in donor acceptor separation are also expected to be especially evident for tension sensors, which, unlike most two-state, on-off, FRET biosensors, are meant to measure a distribution of mechanical loads with potentially varying degrees of fluctuations as the probe is extended.³⁸ Thus, our ability to discern the $\sim 9\%$ difference in FRET efficiency between the unloaded TSMod sensor and its loaded counterpart embedded within VinTS constitutes a markedly finer measurement than detecting the 40% difference in FRET efficiency between the soluble high (GGS) and low (TRAF) FRET standards. The current sensitivity of the system may be estimated from the standard deviation of the TSMod FRET efficiency measurements in Fig. 6, or $\mathrm{\Delta }{E}_{\text{FRET}}\sim \pm 5\%$. Since we expect the TSMod to be unloaded everywhere with negligible variability in the length of the linker, this standard deviation reflects our experimental error (due to both the FLIM system and biological noise), and therefore represents the current measurement uncertainty within a living cell. A 5% variance in $E_{\text{FRET}}$ provides sufficient sensitivity to detect biologically relevant measurements typically made in mechanotransduction experiments with $E_{\text{FRET}}$ changes on the order of 5% to 20%.^10,38,39

The apparent lifetime measured by our system was further converted to an “apparent” $E_{\mathrm{FRET}}^{\mathrm{app}}$ value, which exhibited a linear relationship with the expected $E_{\text{FRET}}$ for the soluble FRET constructs (Fig. 6). The slope of this line was between 0.92 and 0.99 with an $R$-squared value of 0.98. This suggests that the $E_{\mathrm{FRET}}^{\mathrm{app}}$ measurements based on the apparent lifetime are within 1% to 8% of the expected values. A priori, the constructs consist of populations with multiple fluorescent lifetimes. Thus, it is not surprising that our FLIM-based $E_{\mathrm{FRET}}^{\mathrm{app}}$ values are slightly different from the expected $E_{\text{FRET}}$. But furthermore, the linear relationship in Fig. 6 may be used as a calibration curve to convert $E_{\mathrm{FRET}}^{\mathrm{app}}$ to true (expected) $E_{\text{FRET}}$. Applying this calibration results in an average $E_{\text{FRET}}$ of 18% to 19.5% for VinTS and is corroborated by published FRET efficiency values for VinTS in adherent cells.³¹

By investigating the relationship between the measured signal intensity, number of emission photons, and variability in our lifetime measurements, we established that $\sim 300$ photons are required for reproducible lifetime measurements. Finally, the lifetime measurements remained within 2.9% of the initial values after continuous illumination for 120 s with a power of $25\mu \mathrm{W}$ at the sample. Thus, our lifetime images collected with a pixel dwell time on the order of at most tens of microseconds are largely free of photobleaching artifact. For samples expressing soluble FRET constructs with signal typically an order of magnitude higher than VinTS, we were able to achieve high-speed ($128\times 128$ images at $\sim 9\mathrm{fps}$) and high pixel density ($2048\times 2048$ images at $\sim 28\mathrm{s}/\text{frame}$) lifetime imaging using a $6.8\text{-}\mu \mathrm{s}$ pixel dwell time. For VinTS, we used $1024\times 1024$ with a $27.2\text{-}\mu \mathrm{s}$ pixel dwell time.

Calculated $E_{\mathrm{FRET}}^{\mathrm{app}}$ values based on apparent lifetime may be used to measure relative changes in FRET efficiency to compare experimental and control biological conditions. However, quantifying the true value of the FRET efficiency may be central to the conversion of $E_{\text{FRET}}$ to molecular tension in pN.¹⁰ True FRET efficiency quantification may be implemented on a standard epi-fluorescence microscope using the sensitized emission method.^31,34 This method has several drawbacks despite the fact that it might be the most straightforward way to implement FRET in a laboratory where an epi-fluorescence microscope already exists. Due to the overlap between the fluorescence excitation and emission spectra of the donor and acceptor, the FRET signal must be measured in the presence of background noise due to donor and acceptor bleedthrough in the FRET channel. In addition, normalization to fluorophore concentration as well as calibration of the instrument must be achieved in order to convert the measured raw signal to FRET efficiency.³⁴

A more direct method to measure FRET relies on measuring changes in the donor’s fluorescence lifetime in the presence of the acceptor (${\tau }_{\mathrm{DA}}$), relative to the donor’s lifetime in the absence of the acceptor (${\tau }_D$). In this case, the FRET efficiency is given by $E_{\text{FRET}}=1-({\tau }_{\mathrm{DA}}/{\tau }_D)$ for donor–acceptor pairs separated by a constant radius.¹² However, for most FRET constructs in which donor and acceptor pairs are connected via a flexible linker, a distribution of radii exists in the population of molecules being probed.^12,33 Therefore, this distribution gives rise to multiple fluorescence lifetimes within the molecular population being probed. To account for this in FD FLIM systems, the phase and modulation depth of the fluorescence emission are typically measured at multiple modulation frequencies and fit to equations which can account for multiexponential decays.¹⁹ The “amplitude-weighted” average fluorescence lifetime [Eqs. (4.30) and (4.31) in Ref. 12], rather than the intensity-weighted lifetime, may then be used to calculate the average $⟨{\tau }_{\mathrm{DA}}⟩$, from which $E_{\text{FRET}}$ may be inferred. This approach was previously validated by measuring the amplitude-weighted lifetime of high and low FRET standards similar to those used here.³⁷ Nonetheless, compared to measuring a single lifetime, the requirement to probe the system at multiple frequencies, followed by data fitting, lengthens data acquisition time and limits fast FLIM imaging. To enable fast lifetime image acquisition in two separate fluorescence channels, we have used in this paper a single modulation frequency for each excitation channel. A single apparent lifetime value is calculated from the relative phase delay at this modulated frequency using Eq. (12). In addition, we use here the linear relationship in Fig. 6 to calibrate the measured $E_{\mathrm{FRET}}^{\mathrm{app}}$ against the true expected $E_{\mathrm{FRET}}$. This calibration is effectively achieved by measuring the apparent lifetime of a few samples whose known true $E_{\mathrm{FRET}}$ values have been previously measured independently and becomes useful when measuring FRET samples with weak fluorescence signals often resulting in insufficient photons to fit multiexponential decay models unless a long integration time is used. This relationship can then be used to correct for the discrepancy between the apparent FRET efficiency measured at a single modulation frequency and the expected FRET efficiency. In this way, like the sensitized emission method, a single modulation FD instrument would still require additional calibration based on known FRET samples, but it would have the significant added benefit of simplifying the FLIM instrument and allowing faster image acquisition. This is particularly advantageous in applications such as mechanobiology (or others) in which the calibration constructs are similar to the sensors and are readily available. This approach is supported here by our ability to obtain the expected FRET efficiency for the vinculin tension sensor at focal adhesions.³¹ However, further validation is necessary to establish the reproducibility of this approach with other FRET sensors and corroborate the relationship found in Fig. 6. We also note that a monotonic empirical relationship between apparent and true $E_{\mathrm{FRET}}$ that is not linear can still be utilized as a calibration curve in our approach to convert the measured $E_{\mathrm{FRET}}^{\mathrm{app}}$ to true $E_{\mathrm{FRET}}$.

Nonetheless, multiple decay times are still required in FLIM applications whose endpoints are the measurement of multiple lifetimes corresponding to different populations of the same fluorophores in different environments (e.g., free versus protein-bound NADH).^40–43 These applications still require FLIM setups with sufficient temporal resolution to allow measurement of multiple decays. FD-FLIM measurements of modulation and phase at multiple modulation frequencies also allow for robust sample characterization via the phasor plots.⁴² Compared to those instruments, our system is limited to the extent that it does not currently permit measurements of multiple decay times. However, we propose that this limitation does not preclude measuring FRET efficiency and may be circumvented by utilizing the calibration curve in Fig. 6 to convert an unknown sample’s apparent FRET to its corresponding true FRET efficiency. Still, the applicability of this approach beyond the initial VinTS measurement made here remains to be demonstrated. In particular, additional studies may shed more light on the nature of the relationship between apparent and true FRET efficiency observed in Fig. 6, and the potential dependence of this relationship on the choice of another modulation frequency or another fluorescent protein donor–acceptor pair.

In this study, we have used the 520-nm excitation/559-nm emission channel (“AA” channel in Fig. S6 in the Supplementary Material) to provide evidence and measurement of the acceptor (mVenus) fluorescent protein. Alternatively, a FLIM probe may be designed to have a genetically encoded nonfluorescent quencher, such as ShadowG,^44,45 so that the acceptor channel may be replaced by a different channel to view and measure the lifetime of another fluorescent marker in conjunction with the FLIM probe. It is also possible to simultaneously acquire in our system the raw “FRET channel” intensity with excitation at 450 nm and emission at 559 nm (“DA” channel, laser 1, detector 2, $f_1$, in Fig. S6 in the Supplementary Material). This raw FRET signal is not used for FLIM and must be corrected for acceptor and donor bleedthrough. However, this DA channel could be used to measure FRET efficiency based on the sensitized emission-based method after bleedthrough correction and proper calibration as described by Chen et al.³⁴ This, in turn, would allow us to calibrate the $E_{\mathrm{FRET}}^{\mathrm{app}}$ measurement from the apparent lifetime against the FRET efficiency measurement obtained by sensitized emission using the same setup.

Taken together, our results demonstrate the capabilities of a versatile scanning FLIM system that can potentially be adapted for use with a variety of FRET pairs in biological applications. We expect the simple, compact design, and optical throughput of the system, as well as its potential low-cost, to facilitate its dissemination to biological sciences labs. This in turn will advance the study of cell mechanics by allowing end-users to capitalize on the recent advancements in molecular tension probes.