Learning Objectives

Exemplary results of the calibration and live-cell measurements are discussed below. Additionally, the effect of FRET on the cross-correlation curves is demonstrated based on simulated data next to the effect of protein-protein-interaction increasing the CCF_PIE amplitude.

PIE-based FCS data export
In PIE experiments, data are collected in the time-tag time-resolved mode (TTTR)^29,30. Figure 1B shows the photon arrival time histograms of a PIE measurement of a double-labeled DNA strand on the described setup (Supplementary Note 1). The setup has four detection channels. The fluorescence emission is first split by polarization in "S" and "P" directions (referring to the perpendicular and parallel plane in which the electric field of a light wave is oscillating). Secondly, each polarization direction is then split in two color channels (green, red) before detection, resulting in four channels (S-green, S-red, P-green, P-red). In the "prompt" time window, the green fluorophore gets excited, and the signal is detected in both the green and red channels due to FRET. In the delay time window, only the red fluorophore (in the red channel) is visible. Based on the detection channels and "prompt" versus "delayed" time windows, at least five different correlation curves (3 autocorrelation curves (ACFs) and 2 cross-correlation curves (CCFs)) can be obtained (Figure 1C-D): (1) green signal in the prompt time window (ACF_gp), (2) red signal in the prompt time window (in case of FRET, ACF_rp), and (3) red signal in the delay time window (ACF_rd). These ACFs report on the protein mobility, photophysics (e.g., triplet blinking) and other time-correlated brightness changes in the fluorophores (e.g., due to FRET). (4) The PIE-based cross-correlation CCF_PIE of the green signal in the prompt time window with the red signal in the delay time window allows determining the fraction of co-diffusion of the green and red fluorophore¹⁶. (5) The FRET-based cross-correlation CCF_FRET of the green with the red signal in the prompt time window is related to FRET-induced, anticorrelated brightness changes in the green and red signals^31,32,33.

Figure 1: Pulsed-interleaved excitation (PIE) based fluorescence (cross) correlation spectroscopy (F(C)CS). (A) In FCS fluorescently labeled molecules diffuse freely in and out of a (diffraction-limited) focal volume shaped by a focused laser beam that induces fluorescence within this tiny volume. The resulting intensity fluctuations of molecules entering and leaving the volume are correlated and provide information on the mobility of the molecules. (B) In PIE, two different laser lines ("prompt" and "delay") are used to excite the sample labeled with two different fluorophores ("green" and "red"). The time difference between both excitation pulses is adapted to the fluorescence lifetimes of the respective fluorophores so that one has decayed before the other is excited. In the double-labeled sample shown, both fluorophores are sufficiently close to undergo Förster Resonance Energy Transfer (FRET) from the "green" donor fluorophore to the "red" acceptor fluorophore. Thus, red fluorescence emission can be detected in the "prompt" time-window upon excitation of the green donor. In the used setup (Supplementary Note 2), two detectors are used for each color, one oriented parallel to the excitation beam orientation (denoted "p") and the second perpendicular (denoted "s"). (C) Three different autocorrelation functions can be determined in a PIE experiment: Correlation of the i) green channel signals in the prompt time window (ACF_gp), ii) red channel signals in the prompt time window (ACF_rp) and iii) red channel signals in the delay time window (ACF_rd). (D) Two different cross-correlation functions can be determined: iv) The "PIE" cross-correlation (CCF_PIE) with green channel signals in the prompt time window correlated with the red channel signals in the delay window, where the amplitude of this curve is related to the co-diffusion of fluorophores; and v) the "FRET" cross-correlation (CCF_FRET) with the green channel signals in the prompt time window correlated with the red channel signals in the same prompt window; here the shape of this curve at times faster than diffusion is related to the FRET-induced intensity changes. Please click here to view a larger version of this figure.

Calibration
Figure 2A-B shows a calibration measurement of the singly diffusing green and red fluorophores, respectively. Based on a fit with eq. 1 and the known diffusion coefficient D_green²⁶ and D_red²⁷ the shape (z₀ and w₀) and size (V_eff) of the detection volume are calculated using eq. 2a-c. The fit results from the ACF_gp from the green fluorophore and ACF_rd from the red fluorophore are summarized in Figure 2C. Both fluorophores show an additional relaxation time constant of 8.6 µs (18%) and 36 µs (15%), respectively. The molecular brightness (eq. 5a-b) of the green and red fluorophore amounts to 12.5 kHz per molecule and 2.7 kHz per molecule, respectively.

For a reliable estimation of the confocal volume size and shape as well as the molecular brightness, it is recommended to perform 3-5 measurements per calibration experiments and a joint (or global) fit of all repeats.

The crosstalk α (Figure 2D, eq. 3) and the direct excitation of acceptor by the green laser δ (Figure 2E, eq. 4) for this fluorophore pair lie at ~15% and ~ 38%, respectively.

Figure 2: Calibration measurements of freely diffusing green and red calibration standard. (A-B) Representative 60 s measurement of a 2 nM green (A) and a 10 nM red (B) calibration standard measurement fitted to the 3D diffusion model including an additional relaxation time (eq. 1). The table in panel (C) shows the fit results and the derived parameter based on eq. 2a-c and eq. 5a-b. *Diffusion coefficients were taken from literature^26,27. (D) Determination of the crosstalk α of the green signal into the red channels (eq. 3). The excitation spectrum of the green standard is shown in cyan, the emission spectrum in green. The excitation laser lines at 485 nm (blue) and 561 nm (orange) are shown as dashed lines. Transparent green and magenta boxes show the collected emission range (Supplementary Note 2). (E) Determination of the direct excitation δ of the red fluorophore by the 485 nm laser (eq. 4). Color code is identical to (D), light and dark orange show the excitation and emission spectrum of the red standard, respectively. Please click here to view a larger version of this figure.

To determine and calibrate the overlap of the green and red excitation volume, a double-labeled DNA double strand is used (Figure 3A) as described above. Here, the fluorophores are spaced 40 bp apart such that no FRET can occur between the green and red fluorophores attached to the ends of the DNA double strands. Figure 3B shows the autocorrelations from both fluorophores in green (ACF_gp) and magenta (ACF_rd) and the PIE-cross correlation, CCF_PIE, in cyan. Please note that for CCF_PIE, the signal in the green channels in the prompt time window is correlated with the signal in the red channels in the delay time window¹⁶.

Here, an average diffusion coefficient for the DNA strand of D_DNA = 77 µm²/s is obtained. More details on the calculation can be found in the step-by-step protocol, Supplementary Note 4. This value is obtained by inserting the calibrated green and red detection volumes size (Figure 2) and the respective diffusion times of ACF_gp and ACF_rd of the DNA strand (Figure 3C) into equation 2a. Next, using the obtained correction values r_GR and r_RG and using eq. 6 later on, the amount of co-diffusion, i.e., double-labeled molecules (or protein complexes in case of co-transfection of two different proteins) can be determined from the cell samples.

Figure 3: Calibration of the green-red overlap volume using a DNA sample. (A) The DNA strand used for calibration carries a green and a red calibration fluorophore, with a distance of 40 bp in between. The interdye distance must be sufficiently large to exclude FRET between the fluorophores. (B) Representative 60 s measurement of a 10 nM DNA solution. Autocorrelations from both fluorophores in green (ACF_gp, green standard) and magenta (ACF_rd, red standard) and the PIE-crosscorrelation, CCF_PIE, in blue. The table in panel (C) shows the fit results based on the 3D Diffusion model including an additional relaxation term (eq. 1) and the derived parameter diffusion coefficient of DNA, D_DNA (eq. 2a), the size and shape of the overlap volume (eq. 2a-c) and the correction ratios r_GR and r_RG (eq. 6). Please note the values for the green and red detection volume (labeled with *) were taken from the fit of the individual fluorophores shown in Figure 2. Please click here to view a larger version of this figure.

Live-cell experiments
In the following section, the analysis of live-cell experiments for different β₂AR constructs is presented. As β₂AR is a membrane protein, its diffusion is largely limited to a two-dimensional diffusion (Figure 4A) along the cell membrane (except for transport or recycling processes to or from the membrane) ². With the restriction to the 2D diffusion the shape factor s = z₀/w₀ in eq. 1 becomes obsolete resulting in a simplified diffusion model (eq. 9).

Single-labeled constructs: β₂AR-IL3-eGFP and NT-SNAP-β₂AR
Figure 4 shows exemplary measurements of the single-label construct β₂AR-IL3-eGFP (Figure 4B), where eGFP is inserted into the intracellular loop 3, and the construct NT-SNAP-β₂AR (Figure 4C), where the SNAP tag is conjugated to the N-terminus of β₂AR. The SNAP tag is labeled with a membrane-impermeable SNAP surface substrate. The representative curves show the average of 4-6 repeated measurements with acquisition times of 120 – 200 s each. The respective autocorrelations ACF_gp and ACF_rd of the eGFP and SNAP signal are fitted to a bimodal, two-dimensional diffusion model (eq. 9). In terms of fast dynamics, eGFP shows only the expected triplet blinking at t_R1 ~ 9 µs while the SNAP signal requires two relaxation times, one at the typical triplet blinking time of t_R1 ~ 5 µs and a second one at t_R2 ~ 180 µs.

The molecular brightness of the fluorophores in living cells is 0.8 KHz (eGFP) and 1.7 kHz (SNAP) per molecule under the given excitation conditions (eqs. 5a-b). The concentration of the labeled β₂AR constructs incorporated in the cell membrane should be in the nano-molar range and can be determined by the average number of molecules (eq. 9, Figure 4C) and the size of the respective confocal volume for the green and red channel (Figure 2) using eq. 8.

Figure 4: Representative measurement of single-label constructs. (A) In this study, the membrane receptor β₂AR was used as an example. In contrast to the fluorophores and DNA strand used for calibration, which could freely float through the detection volume, membrane proteins diffuse mainly laterally along the membrane, described as 2-dimensional diffusion. (B, D) ACF_gp and ACF_rd of the single-label constructs β₂AR-IL3-eGFP (B) and NT-SNAP-β₂AR (D). Shown is the average of 4-6 measurements each collected for 120 – 200 s. The table in panel (C) shows the fit results of the data to the bimodal two-dimensional diffusion model including additional relaxation terms (eq. 7). Please click here to view a larger version of this figure.

Double-labeled construct: NT-SNAP-β₂AR-IL3-eGFP
In the double-labeled construct NT-SNAP-β₂AR-IL3-eGFP (short NT-SNAP), eGFP is inserted into the intracellular loop 3, and, the SNAP tag conjugated to the N-terminus of β₂AR (Figure 5A). In this configuration, the eGFP is on the inner side of the membrane and the SNAP on the outer side with too large distances for FRET. In an ideal case, this construct would show 100% co-diffusion of the green and red fluorophore, and no FRET signal. Figure 5B-D shows two measurements of the NT-SNAP in two cells on two different measurement days. Fitting the ACF_gp and ACF_rd of the "better" measurement shown in Figure 5B with eq. 7 and the CCF_PIE with eq. 9, reveals 50- 60 molecules in focus for the ACF_gp and ACF_rd, whereas N_app, thus 1/G₀(t_c) ~ 114 for the CCF_PIE (Figure 5C). The concentration of labeled receptors lies in the ~100 nM range as determined with eq. 8. To determine the average concentration of double-labeled molecules, first, the ratio of G₀(t_c) (represented by 1/N_(app)) of the CCF_PIE to ACF_gp and ACF_rd, respectively, is calculated (eq. 6). Next, these values, r_GRcell= 0.43 and r_RGcell = 0.53 are compared to the values obtained from the DNA measurement (r_GR,DNA= 0.51 and r_RG,DNA = 0.79 on this measurement day). Using the rule of proportions, a r_GRcell= 0.43 from the ACF_gp of the eGFP signal reflects to a fraction of co-diffusion (r_GRcell/r_GR,DNA) of 0.84, where for the other case of ACF_rd of the SNAP substrate signal, this value amounts to 0.67. The average concentration of the double-labeled NT-SNAP construct can finally be calculated based on eq. 10. In contrast, in the measurement shown in Figure 5D from a different day, the concentration of receptors is quite low and the data very noisy such that the fit range is limited up to ~ 10 µs. In addition, only a low amount of co-diffusion is observed (15 – 26%).

Figure 5: Double-labeled NT-SNAP-β₂AR-IL3-eGFP construct. (A) In the double labeled construct, the eGFP is inserted into the intracellular loop 3 and the SNAP tag attached to the N-terminus of β₂AR (NT-SNAP). (B, D) ACF_gp, ACF_rd and CCF_PIE of two measurements of the double-labeled construct. The data is fit to a bimodal two-dimensional diffusion model (eq. 9, CCF_PIE) and including additional relaxation terms (eq. 7, ACF_gp and ACF_rd). The table in panel (C) shows the fit results and the derived parameter concentration (eq. 8), the ratio of the correlation amplitude at zero correlation time (G₀(t_c)) and the fraction of co-diffusing molecules (eq. 10). Please note that the measurements were acquired on different days, thus slightly different factor for the amplitude correction were used (B: r_GR,DNA = 0.51 and r_RG,DNA = 0.79; D: r_GR,DNA = 0.51 and r_RG,DNA = 0.56). Please click here to view a larger version of this figure.

Double-labeled construct undergoing FRET: β₂AR-IL3-eGFP-CT-SNAP
In the double-labeled construct β₂AR-IL3-eGFP-CT-SNAP (Figure 6A), the eGFP is inserted into the intracellular loop 3 identical to the NT-SNAP-β₂AR-IL3-eGFP construct with the SNAP tag attached to the C-terminus. Here, both labels are on the same side of the cells' plasma membrane, so that the fluorophores are in close vicinity so that FRET occurs as indicated by the quenched eGFP lifetime (Supplementary Note 5). Considering the flexibility of relatively unstructured protein regions like the C-terminus³⁴ and at least two different protein conformations of GPCRs³⁵, "high FRET" (HF) or "low FRET" (LF), dynamic changes in the FRET efficiency due to eGFP-SNAP distance changes could be observed and identified by an anticorrelation term in the CCF_FRET (orange curve in Figure 6B). FRET fluctuations have been shown to be anticorrelated as the receptor can only be in one state at a time, either HF or LF. Joint (or global) fit of all five correlation curves (Figure 6B) reveals ~70% of slowly diffusing molecules at ~100 ms while the rest diffuses with ~ 1 ms. All autocorrelations and CCF_FRET show relaxation terms at 37 µs and 3 µs; those correlations dominated by red signal (ACF_rp, ACF_rd and CCF_FRET) show an additional slow component ~ 50 ms (Figure 6C).

FRET-induced changes on the CCF_FRET under different conditions (Figure 6D) are demonstrated by a series of simulations of a two-state system with a fluctuation time of 70 µs between LF and HF states. Upon switching from the LF to the HF state, changes in the anticorrelated signal are observed in the prompt time window: The green signal decreases and the red signal increases (vice versa for the HF -> LF switching). If HF-LF switching occurs on timescales faster than the diffusion time, in other words during the residence time of the molecule in the focus, the rate can be derived from the anticorrelation in the CCF_FRET^6,31,36. Please note that dynamic processes slower than the diffusion time cannot be observed in FCS.

In this demonstration, two different FRET scenarios were assumed, showing either a moderate or maximal change in FRET efficiency between the two states. The simulations were performed using Burbulator³⁷ and consider absence or presence of triplet blinking and increasing amount of donor crosstalk into the red channels. The diffusion term was modeled as a bimodal distribution with 30% of fast diffusing molecules at t_D1 = 1 ms and the rest of the molecules diffusing slowly with t_D2 = 100 ms. In total, 10⁷ photons were simulated in a 3D Gaussian-shaped volume with w₀ = 0.5 µm and z₀ = 1.5 µm, a box size of 20, and N_FCS = 0.01.

Figure 6E-F shows the simulation results for the FRET-induced cross-correlation CCF_FRET for moderate (Figure 6E) and maximal FRET contrast (Figure 6F) in the absence (solid lines) and presence of triplet blinking (dashed lines). The FRET-induced anti-correlation can easily be seen in Figure 6F. The "dampening" effect upon adding an additional triplet state reduces the correlation amplitude (Figure 6E-F)^38,39.

Figure 6: Simulation of double-labeled sample showing dynamic FRET. (A) Double-labeled β₂AR with an eGFP inserted into the intracellular loop 3 and a C-terminal SNAP tag. Both fluorophores are close enough to undergo FRET and show changes in the FRET efficiency if the receptor undergoes protein dynamics. (B) Autocorrelation (ACF_gp, ACF_rp and ACF_rd, fit with eq. 7) and cross-correlation curves (CCF_FRET (eq. 7) and CCF_PIE (eq. 9)) of an example measurement. Table in panel (C) shows the fit results. (D-F) To show the influence of experimental parameter on the expected, FRET-induced anticorrelation term, 12 simulations were performed, in which the change in the FRET efficiency (small or large), different amount of donor crosstalk into the acceptor channels (0%, 1% or 10%) and the absence and presence of triplet blinking were modeled. The equilibrium fraction of both FRET-states was assumed to 50:50 and their exchange rates adjusted such that the obtained relaxation time t_R = 70 µs. More details on the simulations see in the text. (E) CCF_FRET of the simulation results with a moderate FRET contrast and in the absence of crosstalk (dark orange), 1% crosstalk (orange) and 10% crosstalk (light orange). Solid lines show results in the absence of triplet, dashed lines in the presence of triplet. (F) CCF_FRET of the simulation results with maximal FRET contrast. The color code is identical to (E). Please click here to view a larger version of this figure.

However, in the simulation most similar to the experimental conditions (α = 10%, 15% triplet blinking and moderate FRET contrast, dashed yellow line in Figure 6E), the anticorrelation term is nearly diminished. Figure 7 shows the result of analyzing this simulated data using the information encoded in the photon arrival time histograms (i.e., the fluorescence lifetime) by means of Fluorescence Lifetime Correlation Spectroscopy (FLCS)^17,19 or species-filtered FCS (fFCS)¹⁸. Here, the fluorescence lifetimes of the known HF and LF species (Figure 7A) are used to generate weights or "filters" (Figure 7B) which are applied during the correlation procedure. In the obtained species-auto- and cross-correlation curves (Figure 7C-D) the anticorrelation can be clearly observed.

Figure 7: Lifetime-filtered FCS can help to uncover the protein dynamics based fluctuations in FRET efficiency in samples with high crosstalk, significant triplet blinking or other photophysical or experimental properties masking the FRET-induced anticorrelation in the CCF_FRET. Here, the approach is shown exemplary for the data shown in Figure 6E for the simulation containing 10% crosstalk and 5% triplet blinking. (A) Normalized fluorescence intensity decay patterns for the two FRET-species (light and dark green for high and low FRET, respectively) and the IRF (grey). The pattern for the parallel detection channel is shown in solid lines, dashed lines for the perpendicular detection channel. (B) The weighting function or "filter" were generated based on the patterns shown in (A), color code is identical to (A). Please note that only the signal in the green detection channels, and thus the FRET-induced donor quenching, is considered here. (C) Four different species-selective correlations are obtained: species-autocorrelations of the low FRET state (sACF_LF-LF, dark green) and the high FRET state (sACF_HF-HF, light green), and the two species-crosscorrelations between the low FRET to the high FRET state (sCCF_LF-HF, dark orange) and vice versa (sCCF_HF-LF, orange). The sCCF clearly shows the anticorrelation in the µs-range. Dashed black lines show the fits. sACF were fit with eq. 9 and sCCF with eq. 11. Table in panel (D) shows the fit results. Please click here to view a larger version of this figure.

CCF_PIE amplitude to study Protein-Protein Interaction (PPI)
Finally, a common use case for PIE-based FCS in live cells is to study the interaction between two different proteins. Here, the read-out parameter is the amplitude of the CCF_PIE, or more precisely the ratio of the autocorrelation amplitudes ACF_gp and ACF_rd to the amplitude of CCF_PIE. To show the effect of increasing co-diffusion on CCF_PIE, simulations have been performed based on the two single-labeled constructs, β₂AR-IL3-eGFP and NT-SNAP-β₂AR (Figure 8A). Figure 8B shows how the amplitude of CCF_PIE increases when the fraction of co-diffusing molecules changes from 0% to 100%. Please note that a 1% crosstalk of green signal into the red channels in the delay time window was added with the diffusion components otherwise modeled as shown above.

Figure 8: The CCF_PIE can be used to study the interaction of two proteins. (A) Here, a co-transfection study of β₂AR-IL3-eGFP with NT-SNAP-β₂AR (carrying a "red" SNAP-label) was simulated. (B) For an increasing amount of co-diffusing molecules (0% (dark blue) -> 100% (light blue)) the amplitude G(t_c) increases. The diffusion term was again modeled as a bimodal distribution with 30% of fast diffusing molecules at t_D1 = 1 ms and the rest of the molecules diffusing slowly with t_D2 = 100 ms. Additionally, 1% crosstalk of green signal into the red delay time window was added. Please click here to view a larger version of this figure.

Table 1: List of variables and abbreviations. For the use of symbols and definition in fluorescence and FRET experiments, the guidelines of the FRET community⁴⁰ are recommended.

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