## Global analysis of time correlated single photon counting FRET-FLIM data

Optics Express, Vol. 17, Issue 8, pp. 6493-6508 (2009)

http://dx.doi.org/10.1364/OE.17.006493

Acrobat PDF (755 KB)

### Abstract

Fluorescence lifetime imaging microscopy (FLIM) can be used to quantify molecular reactions in cells by detecting fluorescence resonance energy transfer (FRET). Confocal FLIM systems based on time correlated single photon counting (TCSPC) methods provide high spatial resolution and high sensitivity, but suffer from poor signal to noise ratios (SNR) that complicate quantitative analysis. We extend a global analysis method, originally developed for single frequency domain FLIM data, with a new filtering method optimized for FRET-FLIM data and apply it to TCSPC data. With this approach, the fluorescent lifetimes and relative concentrations of free and interacting molecules can be reliably estimated, even if the SNR is low. The required calibration values of the impulse response function are directly estimated from the data, eliminating the need for reference samples. The proposed method is efficient and robust, and can be routinely applied to analyze FRET-FLIM data acquired in intact cells.

© 2009 Optical Society of America

## 1. Introduction

1. J. R. Lakowicz, *Principles of Fluorescence Spectroscopy*, 3rd ed. (Springer, 2006). [CrossRef]

2. K. Carlsson, A. Liljeborg, R. M. Andersson, and H. Brismar, “Confocal pH imaging of microscopic specimens using fluorescence lifetimes and phase fluorometry: influence of parameter choice on system performance,” J. Microsc. **199**, 106–114 (2000). [CrossRef] [PubMed]

4. P. I. H. Bastiaens and A. Squire, “Fluorescence lifetime imaging microscopy: spatial resolution of biochemical processes in the cell,” Trends Cell Biol. **9**, 48–52 (1999).' [CrossRef] [PubMed]

5. F. S. Wouters, P. J. Verveer, and P. I. H. Bastiaens, “Imaging biochemistry inside cells,” Trends Cell Biol. **11**, 203–211 (2001). [CrossRef] [PubMed]

5. F. S. Wouters, P. J. Verveer, and P. I. H. Bastiaens, “Imaging biochemistry inside cells,” Trends Cell Biol. **11**, 203–211 (2001). [CrossRef] [PubMed]

10. S. Pelet, M. J. R. Previte, L. H. Laiho, and P. T. C. So, “A fast global fitting algorithm for fluorescence lifetime imaging microscopy based on image segmentation,” Biophys. J. **87**, 2807–2817 (2004). [CrossRef] [PubMed]

11. P. Barber, S. Ameer-Beg, J. Gilbey, R. J. Edens, I. Ezike, and B. Vojnovic, “Global and pixel kinetic data analysis for FRET detection by multi-photon time-domain FLIM,” Proc. SPIE **5700**, 171–181 (2005). [CrossRef]

12. P. Barber, S. Ameer-Beg, J. Gilbey, L. Carlin, M. Keppler, T. Ng, and B. Vojnovic, “Multiphoton time-domain fluorescence lifetime imaging microscopy: practical application to protein-protein interactions using global analysis,” J. R. Soc. Interface **6**, S93–S105 (2008). [CrossRef]

13. P. J. Verveer, A. Squire, and P. I. H. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J. **78**, 2127–2137 (2000). [CrossRef] [PubMed]

14. P. J. Verveer, F. S. Wouters, A. R. Reynolds, and P. I. H. Bastiaens, “Quantitative imaging of lateral ErbB1 receptor signal propagation in the plasma membrane,” Science **290**, 1567–1570 (2000). [CrossRef] [PubMed]

15. P. J. Verveer and P. I. H. Bastiaens, “Evaluation of global analysis algorithms for single frequency fluorescence lifetime imaging microscopy data,” J. Microsc. **209**, 1–7 (2003). [CrossRef] [PubMed]

16. A. H. A. Clayton, Q. S. Hanley, and P. J. Verveer, “Graphical representation and multicomponent analysis of single-frequency fluorescence lifetime imaging microscopy data,” J. Microsc. **213**, 1–5 (2004). [CrossRef]

14. P. J. Verveer, F. S. Wouters, A. R. Reynolds, and P. I. H. Bastiaens, “Quantitative imaging of lateral ErbB1 receptor signal propagation in the plasma membrane,” Science **290**, 1567–1570 (2000). [CrossRef] [PubMed]

17. T. Ng, M. Parsons, W. E. Hughes, J. Monypenny, D. Zicha, A. Gautreau, M. Arpin, S. Gschmeissner, P. J. Verveer, P. I. H. Bastiaens, and P. J. Parker, “Ezrin is a downstream effector of trafficking PKC-integrin complexes involved in the control of cell motility,” EMBO J. **20**, 2723–2741 (2001). [CrossRef] [PubMed]

18. A. R. Reynolds, C. Tischer, P. J. Verveer, O. Rocks, and P. I. H. Bastiaens, “EGFR activation coupled to inhibition of tyrosine phosphatases causes lateral signal propagation,” Nat. Cell Biol. **5**, 447–453 (2003). [CrossRef] [PubMed]

19. O. Rocks, A. Peyker, M. Kahms, P. J. Verveer, C. Koerner, M. Lumbierres, J. Kuhlmann, H. Waldmann, A. Wittinghofer, and P. I. H. Bastiaens, “An acylation cycle regulates localization and activity of palmitoylated Ras isoforms,” Science **307**, 1746–1752 (2005). [CrossRef] [PubMed]

20. G. Xouri, A. Squire, M. Dimaki, B. Geverts, P. J. Verveer, S. Taraviras, H. Nishitani, A. B. Houtsmuller, P. I. H. Bastiaens, and Z. Lygerou, “Cdt1 associates dynamically with chromatin throughout G1 and recruits Geminin onto chromatin,” EMBO J. **26**, 1303–14 (2007). [CrossRef] [PubMed]

21. M. Digman, V. R. Caiolfa, M. Zamai, and E. Gratton, “The Phasor approach to fluorescence lifetime imaging analysis,” Biophys. J. (2007). [PubMed]

22. R. A. Colyer, C. Lee, and E. Gratton, “A novel fluorescence lifetime imaging system that optimizes photon efficiency,” Microsc. Res. Tech. **71**, 201–213 (2008). [CrossRef]

23. S. Padilla-Parra, N. Audugé, M. Coppey-Moisan, and M. Tramier, “Quantitative FRET analysis by fast acquisition time domain FLIM at high spatial resolution in living cells,” Biophys. J. **95**, 2976–2988 (2008). [CrossRef] [PubMed]

## 2. Theory

1. J. R. Lakowicz, *Principles of Fluorescence Spectroscopy*, 3rd ed. (Springer, 2006). [CrossRef]

### 2.1. Fourier analysis of time-domain FLIM data

*Q*exponentials with fluorescence lifetime

*τ*:

_{q}*α*is normalized to one: ∑

_{q}_{q=1}

^{Q}*α*= 1. We assume repetitive excitation with a period

_{q}*T*and write the excitation

*E*(

*t*) as a Fourier series:

*ω*= 2

*π*/

*T*.

*E*

_{0}is real and

*E*=

_{n}*E*

_{n}^{*}, since

*E*(

*t*) is a real-valued signal. The time-resolved response to the excitation defined by Eq. (2) is given by

*F*is the total fluorescence intensity. The normalized result can be written as a Fourier series:

_{T}### 2.2. Global analysis of bi-exponential time-domain FLIM data

*τ*that are invariant. At this point it is useful to define the quantity

_{q}*R*:

_{n,q}*n*, for the single-exponential component

*q*. We assume a set of measurements, indexed with the superscript

*i*, that all have the same fluorescence lifetimes

*τ*, and rewrite Eq. (4) as

_{q}*E*. For the special case of a bi-exponential decay we can write explicitly:

_{n}*α*

_{2}

*=*

^{i}*α*and

^{i}*α*

_{1}

*= 1-*

^{i}*α*, since

^{i}*α*

_{1}

^{i}+

*α*

_{2}

*= 1. We selected*

^{i}*α*to correspond to the fractional fluorescence of the second species for consistency with the analysis of FRET-FLIM data described below. The real and imaginary components of Eq. (8) form two equations from which

^{i}*α*can be eliminated yielding a linear relation between the components of

^{i}*R*:

^{i}_{n}*R*to the linear equation (9) and solving Eqs. (10) for

^{i}_{n}*R*

_{n,1}and

*R*

_{n,2}. Figure 1 shows graphically the principle of this approach using a phasor plot of Im

*R*against Re

^{i}_{n}*R*. All points

^{i}_{n}*R*derived from mono-exponential curves will fall on a half-circle [16

^{i}_{n}16. A. H. A. Clayton, Q. S. Hanley, and P. J. Verveer, “Graphical representation and multicomponent analysis of single-frequency fluorescence lifetime imaging microscopy data,” J. Microsc. **213**, 1–5 (2004). [CrossRef]

24. D. M. Jameson, E. Gratton, and R. Hall, “The measurement and analysis of heterogeneous emissions by multi-frequency phase and modulation fluorometry.” Appl. Spec. Rev. **20**, 55–106 (1984). [CrossRef]

*R*

_{n,1}and

*R*

_{n,2}of this line with the half-circle define the two mono-exponential lifetimes of the mixtures. The lifetimes then follow from Eq. (5):

*α*if

^{i}*R*

_{n,1}and

*R*

_{n,2}are known, but this solution is not optimal for use with experimental data. As shown in Fig. 1, for arbitrary noisy points a better estimation of

*α*is found by the normalized scalar projection of

^{i}*R*on the line connecting

^{i}_{n}*R*

_{n,1}and

*R*

_{n,2}. This turns out to be equivalent to a least squares estimation of

*α*, as was derived before by Verveer

^{i}*et al*. [15

15. P. J. Verveer and P. I. H. Bastiaens, “Evaluation of global analysis algorithms for single frequency fluorescence lifetime imaging microscopy data,” J. Microsc. **209**, 1–7 (2003). [CrossRef] [PubMed]

15. P. J. Verveer and P. I. H. Bastiaens, “Evaluation of global analysis algorithms for single frequency fluorescence lifetime imaging microscopy data,” J. Microsc. **209**, 1–7 (2003). [CrossRef] [PubMed]

16. A. H. A. Clayton, Q. S. Hanley, and P. J. Verveer, “Graphical representation and multicomponent analysis of single-frequency fluorescence lifetime imaging microscopy data,” J. Microsc. **213**, 1–5 (2004). [CrossRef]

25. A. Esposito, H. C. Gerritsen, and F. S. Wouters, “Fluorescence lifetime heterogeneity resolution in the frequency domain by lifetime moments analysis,” Biophys. J. **89**, 4286–4299 (2005). [CrossRef] [PubMed]

26. G. I. Redford and R. M. Clegg, “Polar plot representation for frequency-domain analysis of fluorescence lifetimes,” J. Fluoresc. **15**, 805–815 (2005). [CrossRef] [PubMed]

*R*that can be estimated by Fourier methods if

^{i}_{n}*E*is known, for instance from a reference sample. Such an analysis is based on a single harmonic, even if multiple harmonics are generally available for TCSPC data. This implies that information in the other harmonics is not used, but nevertheless this is sufficient for the important case of fitting bi- exponential decay curves. In principle, any of the harmonics could be used to calculate the two lifetimes

_{n}*τ*

_{1}and

*τ*

_{2}, and the relative fractions

*α*. In this work we have used the first harmonic, since for TCSPC data with pulse-like excitation it is the strongest harmonic, and therefore is expected to have the best SNR.

^{i}### 2.3. The impulse response function

*E*of the excitation

_{n}*E*(

*t*) must be estimated. This can be done using a sample with a known fluorescence lifetime

*τ*(or a scattering sample, where

*τ*= 0). In this case, Eq. (6) is used to estimate

*E*by Fourier analysis, and since

_{n}R_{n}*R*can be calculated from Eq. (5) using the known fluorescence lifetime, the values of

_{n}*E*follow. Here we propose an alternative approach that does not require a reference sample. We assume that the IRF can be approximated by a Gaussian function with standard deviation

_{n}*σ*and a delay

*t*

_{0}:

*ω*and Fourier transformation gives the Fourier coefficients

*E*of a delayed train of Gaussian pulses:

_{n}*E*from the product

_{n}*E*, we assume mono-exponential decay kinetics, and use Eqs. (5) and (14) to write the argument and the absolute value of E

_{n}R_{n}_{n}R

_{n}as:

*t*

_{0}, and the absolute value depends only on the width of the pulse

*σ*. In Fig. 2(a) it can be seen that for higher values of

*n*, the curve for arg(

*E*) is nearly linear. Likewise, Fig. 2(b) shows that the logarithm of ∣

_{n}R_{n}*E*∣ is a near linear function of

_{n}R_{n}*n*

^{2}, for high values of

*n*. We can obtain approximate linear expressions of arg(

*E*) and ln∣

_{n}R_{n}*E*∣, as a function of

_{n}R_{n}*n*and

*n*

^{2}, respectively, by Taylor expansion around an appropriately large harmonic number

*n*

_{0}:

*n*

_{0}is sufficiently large, the contribution of the terms that contain

*τ*can be ignored compared to the terms that contain only

*t*

_{0}or

*σ*, and we find

*a*and

*b*are constant values. Thus

*t*

_{0}and

*σ*can be found by linear fits to the higher harmonic Fourier components. In the case of multi-exponential decays this approach is still valid, since Eqs. (16) are extended with additional terms depending on the fluorescent lifetimes, and will still tend to be linear for high values of

*n*.

*t*

_{0}= 2 ns and

*σ*= 0.1 ns. Linear fitting of the higher Fourier harmonics yielded estimations of

*t*

_{0}= 2.01 ns and

*σ*= 0.188 ns. Thus,

*t*

_{0}was reliably estimated using the linear approximation, but the estimation of

*σ*was inaccurate. This is because the neglected contributions containing the fluorescence lifetimes are larger in the approximation of ln∣

*E*∣ compared to the approximation of arg(

_{n}R_{n}*E*). Rather than extending the range of

_{n}R_{n}*n*, which might not be feasible with experimental data, we used a non-linear fit of Eq. (15b) to estimate

*σ*more reliably. In this fit, the value of

*t*

_{0}was fixed to the value obtained from the linear fit, the initial value of

*σ*was also taken from the linear fit, and an initial value of

*τ*was derived using Eq. (15a). Although the actual data was bi-exponential, a value of

*σ*= 0.099 ns was fitted. Thus, reliable calibration values of

*t*

_{0}and

*σ*can be obtained directly from the FLIM data without additional calibration samples.

### 2.4. Global analysis of FRET-FLIM data

27. G. W. Gordon, G. Berry, X. H. Liang, B. Levine, and B. Herman, “Quantitative fluorescence resonance energy transfer measurements using fluorescence microscopy,” Biophys. J. **74**, 2702–2713 (1998). [CrossRef] [PubMed]

13. P. J. Verveer, A. Squire, and P. I. H. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J. **78**, 2127–2137 (2000). [CrossRef] [PubMed]

14. P. J. Verveer, F. S. Wouters, A. R. Reynolds, and P. I. H. Bastiaens, “Quantitative imaging of lateral ErbB1 receptor signal propagation in the plasma membrane,” Science **290**, 1567–1570 (2000). [CrossRef] [PubMed]

17. T. Ng, M. Parsons, W. E. Hughes, J. Monypenny, D. Zicha, A. Gautreau, M. Arpin, S. Gschmeissner, P. J. Verveer, P. I. H. Bastiaens, and P. J. Parker, “Ezrin is a downstream effector of trafficking PKC-integrin complexes involved in the control of cell motility,” EMBO J. **20**, 2723–2741 (2001). [CrossRef] [PubMed]

18. A. R. Reynolds, C. Tischer, P. J. Verveer, O. Rocks, and P. I. H. Bastiaens, “EGFR activation coupled to inhibition of tyrosine phosphatases causes lateral signal propagation,” Nat. Cell Biol. **5**, 447–453 (2003). [CrossRef] [PubMed]

19. O. Rocks, A. Peyker, M. Kahms, P. J. Verveer, C. Koerner, M. Lumbierres, J. Kuhlmann, H. Waldmann, A. Wittinghofer, and P. I. H. Bastiaens, “An acylation cycle regulates localization and activity of palmitoylated Ras isoforms,” Science **307**, 1746–1752 (2005). [CrossRef] [PubMed]

20. G. Xouri, A. Squire, M. Dimaki, B. Geverts, P. J. Verveer, S. Taraviras, H. Nishitani, A. B. Houtsmuller, P. I. H. Bastiaens, and Z. Lygerou, “Cdt1 associates dynamically with chromatin throughout G1 and recruits Geminin onto chromatin,” EMBO J. **26**, 1303–14 (2007). [CrossRef] [PubMed]

1. J. R. Lakowicz, *Principles of Fluorescence Spectroscopy*, 3rd ed. (Springer, 2006). [CrossRef]

### 2.5. Global analysis of TCSPC data with low SNR

28. F. S. Wouters and P. I. H. Bastiaens, “Fluorescence lifetime imaging of receptor tyrosine kinase activity in cells,” Curr. Biol. **9**, 1127–1130 (1999). [CrossRef] [PubMed]

*R*

_{n,1}, can be estimated, and plotted in a phasor plot as a two-dimensional distribution. The normalized Fourier coefficients

*R*from a sample with donor and acceptor must be found on the straight line that intersects the half-circle of single-exponential values, as illustrated in Fig. 1.

^{i}_{n}*R*is physically acceptable if a straight line through

^{i}_{n}*R*can be found that passes through the donor distribution and that intersects the half-circle at any point to the right of the donor distribution. Strictly, we should use the probability distribution of the mono-exponential donor coeffiecients on the half-circle to calculate a confidence value. In practice, this is difficult with the available distribution of

^{i}_{n}*R*

_{n,1}, which includes multi-exponential points due to noise variation. Instead we adopt a simple geometrical scheme that is illustrated in Fig. 3. We plot a contour line from the Gaussian distribution of the donor coefficients at a given confidence level (for instance at one standard deviation) and find the intersections of this contour with the half-circle of mono-exponential values. Any point

*R*below the line connecting the left-most intersection with the zero-lifetime point on the half-circle,

^{i}_{n}*R*= (0,1), cannot belong to a linear mixture unless its donor lifetime is unlikely to occur, or unless its second lifetime is negative. Likewise any point

_{n}*R*above the line through the left-most intersection, tangent to the half-circle, cannot be part of linear mixture unless its donor lifetime is unlikely or its second lifetime is not intersecting the half-circle (i.e. is not mono-exponential). Thus, we filter the donor/acceptor data by rejecting points that not fulfill these criteria. Furthermore, we exclude points that belong to the donor distribution (i.e. within the donor probability contour) from the set of donor-acceptor points. The result of the filtering is illustrated in Fig. 3, where black circles indicate rejected points. For simplicity, we select the donor probability contour as a circle at a given probability level of a symmetrical 2D Gaussian distribution, which is estimated from the data. The procedure is easily adapted for arbitrary donor distributions, but we found this to be unnecessary. By adjusting the probability level, the filtering can be made less or more stringent. The fluorescence lifetimes can be found from the remaining donor/acceptor points as described before. However, the additional knowledge of the donor distribution can be used to further improve the fit by constraining the mixture line to pass through the estimated mean of the donor coefficients. For an appropriately chosen mono-exponential fluorophore, the distance of the donor mean to the mono-exponential half-circle will be well within the error defined by its distribution, thereby validating its choice as a constraint for the linear fit.

^{i}_{n}## 3. Materials and methods

### 3.1. Simulations

### 3.2. Data analysis

- TCSPC curves are extracted from several data sets, from donor-only samples and from samples with acceptor. Pixels with a total number of photons less than a preset threshold of 20 counts are excluded from the analysis.
- The parameters of the IRF,
*σ*and*t*_{0}, are calculated from the Fourier transform of the average of the selected curves, as described in section 2.3. - The Fourier coefficient of the
*n*th harmonic is calculated from each TCSPC curve:where*b*s the number of counts in the_{k}^{i}*k*th bin of the histogram of photon counts acquired at pixel*i*, and*B*is the total number of used bins. Using Eq. (14) and*σ*and*t*_{0}these Fourier coefficients are corrected for*E*to obtain_{n}*R*.^{i}_{n} - The distribution of
*R*_{n,1}of the donor-only data is estimated by a weighted mean and standard deviation of the real and imaginary parts, to obtain*R*̄_{n,1},*σ*Re*R*_{n,1}and*σ*Im*R*_{n,1}. The weight in each pixel is chosen equal to the square root of the number of photons, which is an estimator for the SNR of a Poisson process (SNR =*N*/√*N*, with N the mean and variance of the Poisson process). - All points from images with donor and acceptor are filtered according to the procedure described in section 2.5, assuming a symmetrical distribution of the donor with mean
*R*̄_{n,1}and standard deviation equal to the average of the estimated standard deviations:*σ**R*_{n,1}= (*σ*Re*R*_{n,1}+*σ*Im*R*_{n,1})/2. - A straight line Im
*R*=^{i}_{n}*u*+_{n}*v*Re_{n}*R*is fit through all remaining donor/acceptor points^{i}_{n}*R*given the constraint that this line should pass through the point^{i}_{n}*R*̄_{n,1}:and the slope*v*is estimated by least squares estimation:where*S*= ∑_{R}Re_{i}w^{i}*R*,^{i}_{n}*S*= ∑_{I}Im_{i}w^{i}*R*,^{i}_{n}*S*= ∑_{RR}(Re_{i}w^{i}*R*)^{i}_{n}^{2},*S*= ∑_{RI}Re_{i}w^{i}*R*Im^{i}_{n}*R*, and^{i}_{n}*S*= ∑_{w}. The weights_{i}w^{i}*w*are chosen equal to 1/^{i}*I*, where^{i}*I*is the total number of counts in pixel^{i}*i*. The calculation of these sums does not require all*R*to be stored in memory simultaneously, and memory requirements are therefore low.^{i}_{n} - In each pixel the fractional fluorescence intensities
*α*of the short lifetime species are found using Eq. (12), and converted to relative concentrations by renormalization with the estimated lifetimes as described by Verveer^{i}*et al*. [13].**78**, 2127–2137 (2000). [CrossRef] [PubMed]

*n*= 1 in steps 3–7.

### 3.3. Sample preparation

*μ*g/ml of PY72, a generic antibody against phosphotyrosine (In vivo Biotech Service, Hennigsdorf, Germany) labeled with Cy3.5. Donor-only samples were prepared by skipping this last step.

### 3.4. Measurement of the impulse response function

### 3.5. TCSPC measurements

## 4. Results

### 4.1. Simulations

*t*

_{0}and

*σ*, calculated from 500 simulations with different noise realizations. The recovery of the IRF parameters shows good agreement with simulated parameters if the mean photon count per pixel is sufficiently high and improves if the number of pixels increases. Thus, these simulations indicate that it is possible to reliably recover the parameters of the IRF from the data, without additional calibration samples.

*α*. As expected, the fit improves as the mean number of counts per pixel increases. At a mean count of a 1000 photons or higher, the filtering procedure is not necessary. With filtering, a reliable fit can be obtained even if the mean photon count per pixel is much lower, removing the systematic error that is observed in the absence of filtering. As expected for a global analysis method, the quality of the result improves as the number of pixels increases. Note also that the errors in the estimated IRF parameters are small and do not prohibit successful global analysis.

### 4.2. Application to FRET in cells

**290**, 1567–1570 (2000). [CrossRef] [PubMed]

28. F. S. Wouters and P. I. H. Bastiaens, “Fluorescence lifetime imaging of receptor tyrosine kinase activity in cells,” Curr. Biol. **9**, 1127–1130 (1999). [CrossRef] [PubMed]

**290**, 1567–1570 (2000). [CrossRef] [PubMed]

*n*. For sufficiently high value of

*n*these data can be well approximated by a linear model. Likewise Fig. 6(b) shows that the logarithm of the absolute value as a function of the square of the harmonic number

*n*is linear for sufficiently high values of

*n*. Figure 6(c) displays the Gaussian pulse shape using the estimated values for delay

*t*

_{0}and the width

*σ*. Also shown in Fig. 6(c) is the experimentally measured IRF of the system. The measured shape of the IRF is distinctly non-Gaussian, and a fit of a bi-exponential model should account for this. The global analysis only uses the first harmonic of the data and therefore we checked if the first harmonic of the measured IRF corresponded to that of the estimated Gaussian pulse. Indeed the value of

*E*

_{1}calculated from Eq. (14) corresponded well to the value obtained by Fourier transformation of the measured IRF (0.895 + 0.446

*j*vs. 0.892 + 0.450

*j*). To visualize this we reconstructed a Gaussian pulse from the first harmonic of the measured IRF using the inverse of Eq. (14). The Gaussian pulse estimated from the data corresponds to the reconstructed Gaussian curve with high accuracy (Fig. 6(c)).

*τ*

_{1}= 3.04 ns. This is comparable to values obtained by wide-field frequency domain FLIM (2.84 ns and 2.87 ns, from phase and modulation, respectively). A standard frequency domain global analysis [16

**213**, 1–5 (2004). [CrossRef]

**290**, 1567–1570 (2000). [CrossRef] [PubMed]

28. F. S. Wouters and P. I. H. Bastiaens, “Fluorescence lifetime imaging of receptor tyrosine kinase activity in cells,” Curr. Biol. **9**, 1127–1130 (1999). [CrossRef] [PubMed]

## 5. Discussion

## Acknowledgment

## References and links

1. | J. R. Lakowicz, |

2. | K. Carlsson, A. Liljeborg, R. M. Andersson, and H. Brismar, “Confocal pH imaging of microscopic specimens using fluorescence lifetimes and phase fluorometry: influence of parameter choice on system performance,” J. Microsc. |

3. | R. M. Clegg, “Fluorescence resonance energy tranfer,” Fluorescence Imaging Spectroscopy and Microscopy |

4. | P. I. H. Bastiaens and A. Squire, “Fluorescence lifetime imaging microscopy: spatial resolution of biochemical processes in the cell,” Trends Cell Biol. |

5. | F. S. Wouters, P. J. Verveer, and P. I. H. Bastiaens, “Imaging biochemistry inside cells,” Trends Cell Biol. |

6. | A. Schönle, M. Glatz, and S. W. Hell, “Four-dimensional multiphoton microscopy with time-correlated single-photon counting,” Appl. Opt. |

7. | W. Becker, A. Bergmann, M. A. Hink, K. König, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. |

8. | M. Peter and S. M. Ameer-Beg, “Imaging molecular interactions by multiphoton FLIM,” Biol. Cell |

9. | E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt. |

10. | S. Pelet, M. J. R. Previte, L. H. Laiho, and P. T. C. So, “A fast global fitting algorithm for fluorescence lifetime imaging microscopy based on image segmentation,” Biophys. J. |

11. | P. Barber, S. Ameer-Beg, J. Gilbey, R. J. Edens, I. Ezike, and B. Vojnovic, “Global and pixel kinetic data analysis for FRET detection by multi-photon time-domain FLIM,” Proc. SPIE |

12. | P. Barber, S. Ameer-Beg, J. Gilbey, L. Carlin, M. Keppler, T. Ng, and B. Vojnovic, “Multiphoton time-domain fluorescence lifetime imaging microscopy: practical application to protein-protein interactions using global analysis,” J. R. Soc. Interface |

13. | P. J. Verveer, A. Squire, and P. I. H. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J. |

14. | P. J. Verveer, F. S. Wouters, A. R. Reynolds, and P. I. H. Bastiaens, “Quantitative imaging of lateral ErbB1 receptor signal propagation in the plasma membrane,” Science |

15. | P. J. Verveer and P. I. H. Bastiaens, “Evaluation of global analysis algorithms for single frequency fluorescence lifetime imaging microscopy data,” J. Microsc. |

16. | A. H. A. Clayton, Q. S. Hanley, and P. J. Verveer, “Graphical representation and multicomponent analysis of single-frequency fluorescence lifetime imaging microscopy data,” J. Microsc. |

17. | T. Ng, M. Parsons, W. E. Hughes, J. Monypenny, D. Zicha, A. Gautreau, M. Arpin, S. Gschmeissner, P. J. Verveer, P. I. H. Bastiaens, and P. J. Parker, “Ezrin is a downstream effector of trafficking PKC-integrin complexes involved in the control of cell motility,” EMBO J. |

18. | A. R. Reynolds, C. Tischer, P. J. Verveer, O. Rocks, and P. I. H. Bastiaens, “EGFR activation coupled to inhibition of tyrosine phosphatases causes lateral signal propagation,” Nat. Cell Biol. |

19. | O. Rocks, A. Peyker, M. Kahms, P. J. Verveer, C. Koerner, M. Lumbierres, J. Kuhlmann, H. Waldmann, A. Wittinghofer, and P. I. H. Bastiaens, “An acylation cycle regulates localization and activity of palmitoylated Ras isoforms,” Science |

20. | G. Xouri, A. Squire, M. Dimaki, B. Geverts, P. J. Verveer, S. Taraviras, H. Nishitani, A. B. Houtsmuller, P. I. H. Bastiaens, and Z. Lygerou, “Cdt1 associates dynamically with chromatin throughout G1 and recruits Geminin onto chromatin,” EMBO J. |

21. | M. Digman, V. R. Caiolfa, M. Zamai, and E. Gratton, “The Phasor approach to fluorescence lifetime imaging analysis,” Biophys. J. (2007). [PubMed] |

22. | R. A. Colyer, C. Lee, and E. Gratton, “A novel fluorescence lifetime imaging system that optimizes photon efficiency,” Microsc. Res. Tech. |

23. | S. Padilla-Parra, N. Audugé, M. Coppey-Moisan, and M. Tramier, “Quantitative FRET analysis by fast acquisition time domain FLIM at high spatial resolution in living cells,” Biophys. J. |

24. | D. M. Jameson, E. Gratton, and R. Hall, “The measurement and analysis of heterogeneous emissions by multi-frequency phase and modulation fluorometry.” Appl. Spec. Rev. |

25. | A. Esposito, H. C. Gerritsen, and F. S. Wouters, “Fluorescence lifetime heterogeneity resolution in the frequency domain by lifetime moments analysis,” Biophys. J. |

26. | G. I. Redford and R. M. Clegg, “Polar plot representation for frequency-domain analysis of fluorescence lifetimes,” J. Fluoresc. |

27. | G. W. Gordon, G. Berry, X. H. Liang, B. Levine, and B. Herman, “Quantitative fluorescence resonance energy transfer measurements using fluorescence microscopy,” Biophys. J. |

28. | F. S. Wouters and P. I. H. Bastiaens, “Fluorescence lifetime imaging of receptor tyrosine kinase activity in cells,” Curr. Biol. |

**OCIS Codes**

(170.1420) Medical optics and biotechnology : Biology

(170.1790) Medical optics and biotechnology : Confocal microscopy

(170.2520) Medical optics and biotechnology : Fluorescence microscopy

(170.3650) Medical optics and biotechnology : Lifetime-based sensing

(170.6280) Medical optics and biotechnology : Spectroscopy, fluorescence and luminescence

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: January 23, 2009

Revised Manuscript: February 26, 2009

Manuscript Accepted: March 10, 2009

Published: April 3, 2009

**Virtual Issues**

Vol. 4, Iss. 6 *Virtual Journal for Biomedical Optics*

**Citation**

Hernan E. Grecco, Pedro Roda-Navarro, and Peter J. Verveer, "Global analysis of time correlated single photon counting FRET-FLIM data," Opt. Express **17**, 6493-6508 (2009)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-17-8-6493

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