## Automated suppression of sample-related artifacts in Fluorescence Correlation Spectroscopy

Optics Express, Vol. 18, Issue 11, pp. 11073-11082 (2010)

http://dx.doi.org/10.1364/OE.18.011073

Acrobat PDF (925 KB)

### Abstract

Fluorescence Correlation Spectroscopy (FCS) in cells often suffers from artifacts caused by bright aggregates or vesicles, depletion of fluorophores or bleaching of a fluorescent background. The common practice of manually discarding distorted curves is time consuming and subjective. Here we demonstrate the feasibility of automated FCS data analysis with efficient rejection of corrupted parts of the signal. As test systems we use a solution of fluorescent molecules, contaminated with bright fluorescent beads, as well as cells expressing a fluorescent protein (ICA512-EGFP), which partitions into bright secretory granules. This approach improves the accuracy of FCS measurements in biological samples, extends its applicability to especially challenging systems and greatly simplifies and accelerates the data analysis.

© 2010 Optical Society of America

## 1. Introduction

*in vitro*as well as

*in vivo*[1–4

1. E. L. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers **13** (1), 1–27 (1974). [CrossRef]

5. T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-Focus Fluorescence Correlation Spectroscopy: A New Tool for Accurate and Absolute Diffusion Measurements,” ChemPhysChem **8**(3), 433–443 (2007). [CrossRef] [PubMed]

6. S. Kim, K. Heinze, and P. Schwille, “Fluorescence correlation spectroscopy in living cells,” Nat. Methods **4**(11), 963–974 (2007). [CrossRef] [PubMed]

7. K. Bacia, S. Kim, and P. Schwille, “Fluorescence cross-correlation spectroscopy in living cells,” Nat. Methods **3**(2), 83–89 (2006). [CrossRef] [PubMed]

8. J. Ries and P. Schwille, “New Concepts for Fluorescence Correlation Spectroscopy on Membranes,” Phys. Chem. Chem. Phys. **10**(24), 3487–3497 (2008). [CrossRef] [PubMed]

9. S. R. Yu, M. Burkhardt, M. Nowak, J. Ries, Z. Petrásek, S. Scholpp, P. Schwille, and M. Brand, “Fgf8 morphogen gradient forms by a source-sink mechanism with freely diffusing molecules,” Nature **461**(7263), 533–536 (2009). [CrossRef] [PubMed]

4. K. Bacia and P. Schwille, “A dynamic view of cellular processes by in vivo fluorescence auto-and cross-correlation spectroscopy,” Methods **29**(1), 74–85 (2003). [CrossRef] [PubMed]

*in vivo*systems, often a two-component diffusion or anomalous diffusion has to be assumed. Including a third component for distortions usually results in too many free parameters and indefinite fit results. Finally, large parts of the data are discarded leading to additional noise on the correlation curves.

*in vivo*high-throughput FCS screens.

## 2. Theory

### 2.1. Model functions

*I*(

*t*) is recorded with a high temporal resolution. From this signal, the auto-correlation curve

*G*(

*τ*), which measures its self similarity, can be calculated:

*δI*(

*t*) =

*I*(

*t*) − 〈

*I*(

*t*)〉.

*τ*is called the lag time. The calculation of the auto-correlation curve from the fluorescence intensity [Eq. (1)] can be performed efficiently on a quasi-logarithmic time scale with a ‘multiple tau’ correlation algorithm [10

10. D. Magatti and F. Ferri, “Fast multi-tau real-time software correlator for dynamic light scattering,” Appl. Opt. **40**(24), 4011–4021 (2001). [CrossRef]

3. E. P. Petrov and P. Schwille, *State of the art and novel trends in fluorescence correlation spectroscopy, in: Standardization in Fluorometry: State of the Art and Future Challenges*, (Springer, Berlin Heidelberg New York, 2007).
[PubMed]

*N*=

*V*

_{eff}

*C*is the number of particles in the detection volume

*V*

_{eff}=

*π*

^{3/2}

*Sw*

^{3}

_{0},

*w*

_{0}is the 1/

*e*

^{2}-radius of the laser focus and structure parameter

*S*=

*w*/

_{z}*w*

_{0}measures the aspect ratio of the Gaussian detection volume.

*τ*=

_{D}*w*

^{2}

_{0}/4

*D*is the diffusion time and a measure for the diffusion coefficient

*D*.

*τ*

_{D1}and

*τ*

_{D2}, taking into account triplet/blinking kinetics and assuming the same brightness of the molecules the correlation function is:

### 2.2. Automated analysis of FCS data

*I*(

*t*), ordering of the curves based on their deviation from the other curves and averaging of the curves with the smallest deviation:

- Division of the fluorescence intensity trace
*I*(*t*) of length*T*into_{M}*n*=*T*/Δ_{M}*T*short intervals (time windows)*I*(_{k}*t*) of length Δ*T*. Δ*T*can be much smaller and*n*much larger than practical for hand-selection. - Calculation of
*n*correlation curves*G*(_{k}*τ*) from the short intensity traces_{i}*I*(_{k}*t*) with a reduced time resolution using a multiple tau correlation algorithm. The choice of a minimal lag-time*τ*^{min}≈ 0.1*τ*_{D1}has the advantage that calculation times are reduced and that the parts at smaller*τ*, where the shot noise (random noise on the curve) dominates the correlation curve, is not considered for the following ordering step. - Ordering of the curves according to their deviation from the average:
- Make a list of all curves.
- For all
*k*compare*G*(_{k}*τ*) with the average of all other_{i}*G*_{j≠k}(*τ*) in the list. As a measure for the difference we use:_{i}〈〉_{j≠k}denotes the average over all curves*j*≠*k*, 〈〉is the average over all lag times_{i}*τ*._{i} - Determine maximum difference
*dG*= max(_{m}*dG*)._{k} - Store
*dG*and the index_{m}*m*. - Remove
*m*from the list. - Continue with step 3b until the list is empty.
- At the end of step 3 all curves are sorted according to their quantitative deviation from the average.

- Chose maximum allowed
*dG*^{max}. How to chose*dG*^{max}will be discussed in more detail below. After this step we have eliminated the irregular curves. - For all
*dG*<_{m}*dG*^{max}calculate the corresponding correlation curves*G̃*(_{m}*τ*) with the full time resolution._{i} - Average all
*G̃*(_{m}*τ*)._{i}

### 2.3. Length of time interval ΔT

*T*be? A small Δ

*T*increases the number of correlation curves and therefore the usable portion of the data. In addition, a residual change of the average intensity during Δ

*T*will be reduced. However, when Δ

*T*is too small the shot noise becomes the dominating noise on the correlation curve and conceals the distortions. As a result the sorting algorithm fails. Also, traces that are too short (Δ

*T*≪ 10

^{5}

*τ*, where

_{D}*τ*is the timescale of interest, e.g. the diffusion time of the single molecules) result in a systematic bias [11

_{D}11. A. Tcherniak, C. Reznik, S. Link, and C. F. Landes, “Fluorescence correlation spectroscopy: criteria for analysis in complex systems,” Anal. Chem. **81**(2), 746–754 (2009). [CrossRef]

*T*should be chosen which is large enough that this bias is avoided and for which the shot noise is not larger than the deviations due to distortions on the time scale evaluated during the sorting algorithm. Visual inspection of correlation curves from a typical measurement, calculated on different time intervals Δ

*T*, will help finding an optimal value for this parameter.

### 2.4. Maximum difference dG^{max}

*dG*

^{max}defines what distortions are still allowed. A large

*dG*

^{max}results in better statistics and lower noise on the correlation curves at the expense of a larger influence of distortions. If

*dG*

^{max}is so small that only a few curves are left, the average curve will be very noisy and a possible bias can occur [Figs. 2(e)–2(g)].

*dG*

^{max}we suggest plotting the fitted parameters of interest (e.g.

*τ*,

_{D}*N*) in dependence of

*dG*

^{max}for a few curves of a dataset and to determine the range in which these parameters are constant [Figs. 2(e)–2(g)]. Another option is to measure homogeneous control samples to determine the range of naturally occurring

*dG*. We found that the optimal

_{m}*dG*

^{max}was usually about one order of magnitude above the minimum of

*dG*[Fig. 2(h)]. It is a merit of this approach that the dependence of the parameters of interest (e.g.

_{m}*τ*,

_{D}*N*) on the exact choice of

*dG*

^{max}is very small.

## 3. Results and Discussion

### 3.1. FCS on Streptavidin-Atto565 with fluorescent beads

*τ*

_{D1}= 0.09 ms, 10s intervals and

*τ*

_{D1}= 0.10 ms, 1 s intervals) very different from the control consisting of only Streptavidin-Atto565 without beads (

*τ*= 0.185 ms). The curve extracted with the automated selection algorithm described above resulted in a correlation curve hardly distinguishable from the control

_{D}*τ*= 0.185 ms).

_{D}*τ*= 0.76 ± 0.95 ms, 10 s interval and

_{D}*τ*= 0.16 ± 0.09 ms, 1 s interval), whereas the automatically processed curves lead to very reproducible parameter estimates (

_{D}*τ*= 0.181 ± 0.007 ms,

_{D}*F*= 0.953 ± 0.016). Even for the samples with a large amount of beads, where only 10% of the data could be used to construct the final correlation curve, the fit parameters were consistent (

*τ*= 0.180 ms,

_{D}*F*= 0.951).

### 3.2. FCS on ICA512-EGFP in Ins-1 cells

12. M. Asfari, D. Janjic, P. Meda, G. Li, P. A. Halban, and C. B. Wollheim, “Establishment of 2-mercaptoethanol-dependent differentiated insulin-secreting cell lines,” Endocrinology **130**(1), 167–178 (1992). [CrossRef] [PubMed]

13. M. Trajkovski, H. Mziaut, A. Altkruger, J. Ouwendijk, K. P. Knoch, S. Muller, and M. Solimena, “Nuclear translocation of an ICA512 cytosolic fragment couples granule exocytosis and insulin expression in beta-cells,” J. Cell. Biol. **167**(6), 1063–1074 (2004). [CrossRef] [PubMed]

### 3.3. Dependence of fit parameters on dG^{max}

*dG*

^{max}on the parameter estimates we used the selection algorithm to order the curves calculated on short intervals of the fluorescence intensity, determined the average of a fraction of the curves with the smallest

*dG*and fitted this average with a two-component fit including triplet (Streptavidin-Atto565 with fluorescent beads and ICA512-EGFP with bright granules) or a one-component fit with fixed triplet (controls).

_{m}*dG*, a measure for the difference between the last curve used and the average of the other curves [Eq. (4)], spanned about one order of magnitude [Fig. 2(h)]. This can be considered the variation of

_{m}*dG*in samples not influenced by distortions, suggesting a choice of

_{m}*dG*

^{max}≈ 10×min(

*dG*).

_{m}*dG*spanned several orders of magnitude [Fig. 2(h)]. Due to the higher number of free fitting parameters (in addition to

_{m}*N*and

*τ*in the control case now also the triplet fraction

_{D}*T*, the fast fraction

*F*and the diffusion time of the slow fraction

*τ*

_{D2}were varied during the fit), their variation was in general increased. Apart from this noise,

*N*and

*τ*remained constant over a surprisingly large range of

_{D}*dG*

^{max}, even for values of

*dG*

^{max}significantly larger than the suggested ≈ 10×min(

*dG*) where the slow fraction became significant. Only inclusion of more than 70% of the curves lead to a significant deviation of the parameters.

_{m}*τ*was visible already much earlier when more than 70% of the curves were discarded. The reason was mainly due to the triplet/blinking part: if fewer curves are considered, the higher noise on the curves results in a poorly defined triplet/blinking fraction

_{D}*T*. Accordingly, in this range

*T*showed strong deviations (data not shown). Fixing

*T*during the fitting reduced these deviations. However, this also decreased the range over which

*τ*remained unaltered — due to the large number of fluorophores in vesicles or fluorescent beads these entities do not exhibit a significant triplet/blinking. If their contribution to the correlation curve becomes larger, the overall triplet/blinking fraction

_{D}*T*is reduced.

### 3.4. Limitations

*T*, since only unaffected parts of the data are used to construct the final curve. If the density of bright aggregates or vesicles is so high that every time interval is affected, this approach fails. On the other hand, a minimum length of the time windows is required to reduce the shot noise on the correlation curves sufficiently, such that distortions become detectable. If bright events are sparse, the time windows can be chosen longer and samples with lower molecular brightness and hence stronger noise on the correlation curves can be analyzed.

8. J. Ries and P. Schwille, “New Concepts for Fluorescence Correlation Spectroscopy on Membranes,” Phys. Chem. Chem. Phys. **10**(24), 3487–3497 (2008). [CrossRef] [PubMed]

### 3.5. Comparison to other approaches

14. C. C. Guet, L. Bruneaux, T. L. Min, D. Siegal-Gaskins, I. Figueroa, T. Emonet, and P. Cluzel, “Minimally invasive determination of mRNA concentration in single living bacteria,” Nucleic Acids Res. **36**(12), e73 (2008). [CrossRef] [PubMed]

15. G. Meacci, J. Ries, E. Fischer-Friedrich, N. Kahya, P. Schwille, and K. Kruse, “Mobility of Min-proteins in Escherichia coli measured by fluorescence correlation spectroscopy,” Phys. Biol. **3**(4), 255–263 (2006). [CrossRef]

*T*. The influence of the exact choice of the parameters and the model on the outcome of the selection is not clear. A direct selection of curves prior to fitting might therefore be more suited to distinguish between different possible models.

*t*, is larger than a cut-off

_{b}*I*

^{max}. The performance of this algorithm in rejecting distortions was only slightly below that of the sorting algorithm presented in this work, but required a careful choice of

*t*and

_{b}*I*

^{max}for every set of measurements. With parameters

*t*and

_{b}*I*

^{max}optimized for every curve, the peak-finding algorithm resulted in a fast fraction

*F*a few percent lower than that obtained with the sorting algorithm.

*τ*was similar within the fitting error. Apart from its dependence on empirical parameters a drawback of the peak-finding algorithm is that it might fail to detect peripheral transits or low brightness vesicles, mistake shot noise in the intensity for an irregular event and does not remove distortions due to instabilities or photobleaching.

_{D}*T*and can therefore sample large parts of the data and, most importantly, it does not depend strongly on empirical parameters which renders it easy to use.

## 4. Materials and Methods

### 4.1. Fluorescence Correlation Spectroscopy

*μ*W of the 561 laser line and 3.2

*μ*W of the 488 laser line were used. For measurements on ICA512-EGFP 8.1

*μ*W of the 488 nm laser line were used. The raw data of photon arrival times were stored and further processed.

### 4.2. Data analysis

### 4.3. Ins-1 cells

13. M. Trajkovski, H. Mziaut, A. Altkruger, J. Ouwendijk, K. P. Knoch, S. Muller, and M. Solimena, “Nuclear translocation of an ICA512 cytosolic fragment couples granule exocytosis and insulin expression in beta-cells,” J. Cell. Biol. **167**(6), 1063–1074 (2004). [CrossRef] [PubMed]

## 5. Conclusion

## Acknowledgements

## References and links

1. | E. L. Elson and D. Magde, “Fluorescence correlation spectroscopy. I. Conceptual basis and theory,” Biopolymers |

2. | R. Rigler and E. Elson, |

3. | E. P. Petrov and P. Schwille, |

4. | K. Bacia and P. Schwille, “A dynamic view of cellular processes by in vivo fluorescence auto-and cross-correlation spectroscopy,” Methods |

5. | T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, “Two-Focus Fluorescence Correlation Spectroscopy: A New Tool for Accurate and Absolute Diffusion Measurements,” ChemPhysChem |

6. | S. Kim, K. Heinze, and P. Schwille, “Fluorescence correlation spectroscopy in living cells,” Nat. Methods |

7. | K. Bacia, S. Kim, and P. Schwille, “Fluorescence cross-correlation spectroscopy in living cells,” Nat. Methods |

8. | J. Ries and P. Schwille, “New Concepts for Fluorescence Correlation Spectroscopy on Membranes,” Phys. Chem. Chem. Phys. |

9. | S. R. Yu, M. Burkhardt, M. Nowak, J. Ries, Z. Petrásek, S. Scholpp, P. Schwille, and M. Brand, “Fgf8 morphogen gradient forms by a source-sink mechanism with freely diffusing molecules,” Nature |

10. | D. Magatti and F. Ferri, “Fast multi-tau real-time software correlator for dynamic light scattering,” Appl. Opt. |

11. | A. Tcherniak, C. Reznik, S. Link, and C. F. Landes, “Fluorescence correlation spectroscopy: criteria for analysis in complex systems,” Anal. Chem. |

12. | M. Asfari, D. Janjic, P. Meda, G. Li, P. A. Halban, and C. B. Wollheim, “Establishment of 2-mercaptoethanol-dependent differentiated insulin-secreting cell lines,” Endocrinology |

13. | M. Trajkovski, H. Mziaut, A. Altkruger, J. Ouwendijk, K. P. Knoch, S. Muller, and M. Solimena, “Nuclear translocation of an ICA512 cytosolic fragment couples granule exocytosis and insulin expression in beta-cells,” J. Cell. Biol. |

14. | C. C. Guet, L. Bruneaux, T. L. Min, D. Siegal-Gaskins, I. Figueroa, T. Emonet, and P. Cluzel, “Minimally invasive determination of mRNA concentration in single living bacteria,” Nucleic Acids Res. |

15. | G. Meacci, J. Ries, E. Fischer-Friedrich, N. Kahya, P. Schwille, and K. Kruse, “Mobility of Min-proteins in Escherichia coli measured by fluorescence correlation spectroscopy,” Phys. Biol. |

**OCIS Codes**

(170.0170) Medical optics and biotechnology : Medical optics and biotechnology

(170.1420) Medical optics and biotechnology : Biology

(170.1530) Medical optics and biotechnology : Cell analysis

(170.1790) Medical optics and biotechnology : Confocal microscopy

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

(180.0180) Microscopy : Microscopy

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: March 30, 2010

Revised Manuscript: April 19, 2010

Manuscript Accepted: April 21, 2010

Published: May 11, 2010

**Virtual Issues**

Vol. 5, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

Jonas Ries, Mathias Bayer, Gábor Csúcs, Ronald Dirkx, Michele Solimena, Helge Ewers, and Petra Schwille, "Automated suppression of
sample-related artifacts in Fluorescence
Correlation Spectroscopy," Opt. Express **18**, 11073-11082 (2010)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-11-11073

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### References

- E. L. Elson and D. Magde, "Fluorescence correlation spectroscopy. I. Conceptual basis and theory," Biopolymers 13 (1), 1-27 (1974). [CrossRef]
- R. Rigler and E. Elson, Fluorescence Correlation Spectroscopy: Theory and Applications, (Springer, 2001). [CrossRef]
- E. P. Petrov and P. Schwille, State of the art and novel trends in fluorescence correlation spectroscopy, in: Standardization in Fluorometry: State of the Art and Future Challenges, (Springer, Berlin Heidelberg New York, 2007). [PubMed]
- K. Bacia and P. Schwille, "A dynamic view of cellular processes by in vivo fluorescence auto-and crosscorrelation spectroscopy," Methods 29(1), 74-85 (2003). [CrossRef] [PubMed]
- T. Dertinger, V. Pacheco, I. von der Hocht, R. Hartmann, I. Gregor, and J. Enderlein, "Two-Focus Fluorescence Correlation Spectroscopy: A New Tool for Accurate and Absolute Diffusion Measurements," ChemPhysChem 8(3), 433-443 (2007). [CrossRef] [PubMed]
- S. Kim, K. Heinze, and P. Schwille, "Fluorescence correlation spectroscopy in living cells," Nat. Methods 4(11), 963-974 (2007). [CrossRef] [PubMed]
- K. Bacia, S. Kim, and P. Schwille, "Fluorescence cross-correlation spectroscopy in living cells," Nat. Methods 3(2), 83-89 (2006). [CrossRef] [PubMed]
- J. Ries and P. Schwille, "New Concepts for Fluorescence Correlation Spectroscopy on Membranes," Phys. Chem. Chem. Phys. 10(24), 3487-3497 (2008). [CrossRef] [PubMed]
- S. R. Yu,M. Burkhardt, M. Nowak, J. Ries, Z. Petr’asek, S. Scholpp, P. Schwille, and M. Brand, "Fgf8 morphogen gradient forms by a source-sink mechanism with freely diffusing molecules," Nature 461(7263), 533-536 (2009). [CrossRef] [PubMed]
- D. Magatti and F. Ferri, "Fast multi-tau real-time software correlator for dynamic light scattering," Appl. Opt. 40(24), 4011-4021 (2001). [CrossRef]
- A. Tcherniak, C. Reznik, S. Link, and C. F. Landes, "Fluorescence correlation spectroscopy: criteria for analysis in complex systems," Anal. Chem. 81(2), 746-754 (2009). [CrossRef]
- M. Asfari, D. Janjic, P. Meda, G. Li, P. A. Halban, and C. B. Wollheim, "Establishment of 2-mercaptoethanoldependent differentiated insulin-secreting cell lines," Endocrinology 130(1), 167-178 (1992). [CrossRef] [PubMed]
- M. Trajkovski, H. Mziaut, A. Altkruger, J. Ouwendijk, K. P. Knoch, S. Muller, and M. Solimena, "Nuclear translocation of an ICA512 cytosolic fragment couples granule exocytosis and insulin expression in beta-cells," J. Cell. Biol. 167(6), 1063-1074 (2004). [CrossRef] [PubMed]
- C. C. Guet, L. Bruneaux, T. L. Min, D. Siegal-Gaskins, I. Figueroa, T. Emonet, and P. Cluzel, "Minimally invasive determination of mRNA concentration in single living bacteria," Nucleic Acids Res. 36(12), e73 (2008). [CrossRef] [PubMed]
- G. Meacci, J. Ries, E. Fischer-Friedrich, N. Kahya, P. Schwille, and K. Kruse, "Mobility of Min-proteins in Escherichia coli measured by fluorescence correlation spectroscopy," Phys. Biol. 3(4), 255-263 (2006). [CrossRef]

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