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Modulation Filtering Enables Removal of Spikes in Fluorescence Correlation Spectroscopy Measurements without Affecting the Temporal Information Gustav Persson, Per Thyberg, Tor Sande´n, and Jerker Widengren* Department of Applied Physics, Experimental Biomolecular Physics, Royal Institute of Technology, SE-106 91 Stockholm, Sweden ReceiVed: March 20, 2009; ReVised Manuscript ReceiVed: May 5, 2009
The appearance of intensity spikes in measurements is a common problem in fluorescence correlation spectroscopy (FCS) studies of biological samples. In this work, we present a new method for generating artifact-free correlation curves from fluorescence traces that have undergone spike removal. This method preserves the temporal information throughout the measurement and properly represents the correlation between events separated by removed spikes. The method was validated using experimental data. The proposed algorithm is demonstrated herein to be generally applicable, but it is particularly powerful for cases where spikes occur frequently. Introduction 1
Fluorescence correlation spectroscopy (FCS) is a versatile method that makes use of fluorescence intensity fluctuations for characterizing the dynamics of a low number of molecules moving through a very small detection volume, normally the laser focus in a confocal microscope. FCS can be used to monitor a range of dynamic molecular processes that affect the fluorescence intensity, without any need to perturb the system under study. It has been used in numerous biophysical studies and has found many applications in analytical chemistry and biochemistry.2-7 The small detection volume and the noninvasiveness of FCS also make it highly suitable for measurements in live cells. However, a common problem, particularly when FCS is used for studies of biological samples, is the appearance of spikes, that is, sudden large transient increases of the measured fluorescence intensity. These can occur, for example, as a result of aggregation of the molecules of interest or natural presence of or contamination by strongly fluorescent or reflecting particles. Because of the nature of the correlation function used in FCS, all fluorescent entities contribute to the measurement results proportionally to the square of their fluorescence brightness.8 A few short intense spikes, or even a single one, can thus render a long measurement useless. Sometimes, spikes can be eliminated by very careful sample preparation, but in many cases, this is not possible. Therefore, the option of removing the effects of spikes after the measurement has been made is very attractive. In this work, we present a new method for generating an artifact-free correlation curve from a fluorescence trace from which spikes have been removed. This method is based on the theory developed for FCS measurements with time-modulated excitation9 and preserves the temporal information throughout the measurement. The method is demonstrated on experimental data and compared with other approaches for the treatment of fluorescence traces after spike removal. Because the preceding spike identification is not the focus of this study, a very simple algorithm was chosen for the identification of spikes in the * To whom correspondence should be addressed. E-mail: jerker@ biomolphysics.kth.se. Phone: +46-8-5537 8030. Fax: +46-8-5537 8216.
measurements used for the demonstration. Despite the simplicity of the spike identification, the proposed approach was found to reliably restore correlation curves that generated fit parameters nearly identical to those of a clean sample. With a properly chosen model function, the goodness of fit could even aid the selection of spike identification parameters, as all observed deviations from the model could be attributed to imperfect spike removal. The presented method preserves correlations between events before and after a removed spike, which is of particular interest if very short intense spikes appear in the measurement or if spikes occur very frequently. Theory In FCS, information is extracted by calculation of the normalized autocovariance of the fluorescence signal I(t), commonly referred to as the autocorrelation function
G(τ) )
〈I(t) I(t + τ)〉 〈I(t)〉〈I(t + τ)〉
(1)
Here, the angle brackets denote averaging over time t, with τ being the lag time or correlation time. G(τ) reports on the characteristic time of the process being studied and the number of fluorescent entities taking part in this process. For homogeneous samples under background-free conditions, the amplitude of the FCS curve is independent of the intensity of the sample fluorescence. In an inhomogeneous sample, however, the contributions from different fractions are weighted by the square of their fluorescence intensities.8 Hence, the contributions of the fluorescent entities of interest might be obscured by large effects on the FCS curve generated by a few bright aggregates. However, if the aggregates are few and the intensity spikes they generate can be identified, it is possible to remove these spikes before calculation of the correlation function. After removing parts of the fluorescence trace, there are at least three different possible ways of generating the correlation curve, which can have different implications for the results. Either the remaining parts of the trace can be joined together and correlated as an intact trace, or each remaining part can be correlated
10.1021/jp902538b CCC: $40.75 2009 American Chemical Society Published on Web 06/02/2009
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Figure 1. Spike removal and rectangular intensity modulation. The red curve is an example of a fluorescence intensity trace containing a spike, and the black curve shows how the same intensity trace could look without the spike. The intensity modulation defined by the blue curve yields the same filtered trace (green curve) when applied to the traces with and without the spike.
separately and the results finally averaged.10 A third possibility presented here, which keeps the time axis intact, is to regard the removal of spikes as a rectangular intensity modulation of the fluorescence signal (Figure 1) and to treat the data accordingly.9 For intensity modulations applied after fluorescence emission, that is, in the detection beam path or electronically or digitally after detection, the registered intensity can be expressed as a product of two uncorrelated components, the modulation M and the emitted fluorescence F
I(t) ) M(t) F(t)
(2)
The autocorrelation function, GI(τ), of the registered intensity can then be expressed as
GI(τ) )
〈I(t) I(t + τ)〉 〈M(t) F(t) M(t + τ) F(t + τ)〉 ) ) 2 〈I〉 〈MF〉2 〈M(t) M(t + τ)〉〈F(t) F(t + τ)〉 (3) 〈M〉2〈F〉2
where the last equality follows from the fact that M and F are uncorrelated. For all τ where 〈M(t) M(t + τ)〉 * 0, we can obtain the autocorrelation function of F by dividing the autocorrelation, GI(τ), of the registered intensity by that of the modulation, GM(τ)9 GF(τ) )
〈I(t) I(t + τ)〉 〈M(t) M(t + τ)〉 〈F(t) F(t + τ)〉 ) ) 〈F〉2 〈I〉2 〈M〉2 GI(τ) (4) GM(τ)
/
The modulation is a train of rectangular pulses of unit height for which the autocorrelation function can be calculated very quickly. If the information remaining in the fluorescence trace after spike removal is representative of the molecules of interest and provides sufficient statistics for all lag times, the modulation filtering will generate a correlation curve identical to one resulting from a measurement on a clean sample. Materials and Methods Experimental Setup. The measurements were performed using a home-built FCS instrument consisting of an Olympus
IX-70 microscope body and a linearly polarized Ar+ ion laser (LGK 7812-1, Siemens AG, Munich, Germany) operated at a wavelength of 488 nm. The laser beam was focused to a 1/e2 radius in the sample of 0.42 µm (estimated from the diffusion time of rhodamine 110) by an Olympus 40×, NA 1.15, UApo/ 340 water-immersion objective. The intensity of the excitation light applied in the presented measurements was 20 µW measured at the entry port of the microscope, which corresponds to an average irradiance in the detection volume of 2.4 kW/ cm2. Emitted fluorescence was collected using the same objective, separated from the excitation light by a dichroic mirror (z488RDC, Chroma Technology Corp., Rockingham, VT) and imaged onto a confocal pinhole of 50-µm diameter by an achromatic lens with 150-mm focal length. After the pinhole, the emission was recollimated, split by a polarizing beam splitter cube into components polarized parallel and perpendicular to the excitation light, spectrally cleaned up by optical band-pass filters (HQ532/70m, Chroma) to remove residual scattered excitation light, and finally focused onto two single-photon avalanche photodiodes (APDs; SPCM-AQR-14/16, PerkinElmer Optoelectronics, Fremont, CA). Data Acquisition and Processing. Data were collected using a PCI-6602 counter/timer card (National Instruments Corporation, Austin, TX), rendering a separate time-tagged photon trace with a resolution of 12.5 ns for each channel by counting pulses from the internal clock between each pair of consecutive photons detected by the corresponding APD. Correlation of the time-tagged photon traces was accomplished by a C program, written in-house based on the algorithm presented by Laurence et al.11 For division of correlation functions and other minor operations, built-in Linux commandline tools were used. The spike detection and removal algorithm, which was implemented in C, was applied directly on the stream of times between consecutive photons. A sliding average was calculated over an adjustable number of interphoton times, the so-called averaging window. If this average, for a certain window, was lower than a set threshold value, all photons contributing to the average were discarded as being part of a spike. For all data presented in this article, the averaging window was set to 50 photons, which is substantially larger than the average number of photons emitted by a free dye molecule during passage through the detection volume, but smaller than the average number of photons generated by the traversal of a liposome containing several fluorophores. The threshold is henceforth expressed as a percentage of the average time between photons in the processed measurement. The beginning and end of each spike was marked in the trace for subsequent modulation filtering. A program for semianalytical correlation of traces consisting of rectangular pulses that was used to generate the filter functions for the modulation filtering of the correlation curves where spikes had been removed was also written in C. This program calculated the correlation function for each pair of rectangular pulses analytically. Given the start and end of each pulse, the contributions of all pulse pairs to each lag time channel were summed, and finally the correlation function was normalized. The Levenberg-Marquardt method was used for nonlinear least-squares fitting of models to the generated correlation curves. All data points were weighted equally, and hence, the reported χ2 values serve only as relative measures of the mean square deviation of the model from the data.
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Sample Preparation. Small unilaminar vesicles (SUVs) were prepared by mixing 2.5 mL of a 10 mg/mL chloroform solution of the glycerophospholipid DOPG {1,2-dioleoyl-sn-glycero-3[phospho-rac-(1-glycerol)], Avanti Polar Lipids, Inc., Alabaster, AL} with 50 µL of a 0.6 µg/mL chloroform solution of Oregon Green-DHPE (Oregon Green 488-1,2-dihexadecanoyl-snglycero-3-phosphoethanolamine, Invitrogen, Carlsbad, CA) in a flask. The ratio of Oregon Green-DHPE to nonfluorescent lipids was 1:106, corresponding to a molar concentration of fluorescent lipids of 0.9 × 10-4 mol %. The number of lipids per liposome was estimated to 1.2 × 104 based on dynamic light scattering measurements and FCS measurements with varying concentration of fluorescent lipids (not presented here), yielding, on average, 1 fluorescent lipid per 100 liposomes. This ensures that a vast majority of the detected fluorescent liposomes are labeled with one single fluorophore. Following evaporation under nitrogen flow, the lipids were dissolved in 4 mL of phosphate-buffered saline (PBS) solution. The lipid mixture was shaken for 30 min, using a vortex mixer, to form multilaminar liposomes and then sonicated, using a tip sonicator, until the solution became transparent. To remove residual dye from the bulk solution, the buffer was changed using a PD10 column (GE Healthcare UK Limited, Little Chalfont, U.K.). The liposome solution was then centrifuged for 40 min at 10000g to remove residual multilaminar liposomes and metal particles from the sonicator tip. The same procedure was repeated to generate multilabeled liposomes by increasing the concentration of Oregon GreenDHPE by factors of 100, 500, and 1000 to yield distributions of number of labels per liposome with averages of 1, 5, and 10, respectively. Oregon Green 488 carboxylic acid succinimidyl ester (Invitrogen) was diluted in PBS to a concentration of 1 nM.
Persson et al.
G(τ) )
(
1 τ 1+ N(1 - T) τD
)( -1
1+
τ β τD 2
)
-1/2
(1 - T +
Te-τ/τT) + 1 (5)
Here, N represents the average number of molecules in the observation volume, and τD is the diffusion time or the average dwell time of a molecule in the observation volume. The ratio of the axial extension and the transverse diameter of the
Results and Discussion Measurements were made on 1 nM free Oregon Green in PBS with different amounts of multilabeled liposomes added to generate spikes with variable frequency. Figure 2 shows the result of one such measurement in comparison with a measurement on free Oregon Green only. In this case, each liposome contained, on average, about 10 Oregon Green molecules, which made it approximately 5 times as bright as free Oregon Green under the present conditions. (Measurements on singly labeled liposomes showed that the fluorophore attached to a liposome is approximately half as bright as the free fluorophore under these conditions.) The concentration of free Oregon Green gave an average of 2.9 dye molecules in the observation volume, and the concentration of liposomes was such that, on average, 18 liposomes passed through the volume each second (on average, 0.06 liposomes in the volume and an average passage time of 3.4 ms, based on FCS measurements on higher concentrations of liposomes and known dilution). As can be seen in Figure 2a, the addition of liposomes strongly affected the correlation curve. It is also evident that removal of intensity spikes and subsequent modulation filtering was capable of removing this effect. In this case, the threshold parameter of the spike removal algorithm was set to 25% of the average time between photons in the measurement. The correlation curve from the measurement on the free dye is well described by a model taking 3-dimensional diffusion and singlet-triplet transitions into account (Figure 2b).12
Figure 2. Filtering of a spiky measurement. (a) FCS curves from measurements on free Oregon Green 488 (black) and the same sample with addition of multilabeled liposomes generating fluorescence intensity spikes (red). After spike removal and modulation filtering of the second measurement, a curve (green) similar to that of the free dye only was obtained. A single diffusion-component model (eq 5) fits (b) the FCS curve from the measurement on free dye (N ) 2.95, τD ) 116 µs, τT ) 1.8 µs, and T ) 0.14), as well as (c) that from the filtered data (N ) 2.86, τD ) 117 µs, τT ) 1.9 µs, and T ) 0.14).
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Figure 3. Spike removal with different threshold values. Correlation curves after spike removal and modulation filtering of data from the same measurement of free Oregon Green 488 with addition of multilabeled liposomes as in Figure 2. The threshold values used are, from top to bottom, 10%, 20%, 30%, 40%, and 50% of the average time between photons.
observation volume is given by the structure parameter β, which was determined by a fit to a reference measurement for each measurement day and fixed for all other fits. T is the average fraction of the molecules residing in the nonfluorescent triplet state, and τT is the characteristic time of equilibration of the populations in the singlet and triplet states. Figure 2c shows a fit of the same model to the filtered curve from the measurement of the mix of free dye and liposomes. This fit generated parameters as similar to the ones above as could be expected from a second measurement on the same sample (see figure caption for values). This agreement confirms that the filtering removed the contribution from the intensity spikes related to liposomes passing through the observation volume without substantially affecting the signal from the free dye molecules. A minor deviation of the data from the model can be observed in the millisecond lag-time range as a result of imperfect spike identification. This is caused by spikes that are undetected by the spike identification algorithm and some remaining influence of spikes on the parts of the fluorescence trace adjacent to the removed intervals. To generate correlation curves representative of selected fluorescence bursts arising from single molecules passing through the detection volume, a substantial part of the fluorescence trace surrounding the detected bursts must be taken into account.13-15 The spike identification itself, however, is not the focus of this work. Because the measurements were made on 50 µL droplets placed directly on microscope coverslips, the small difference in number of molecules N might reflect an actual concentration difference due to the evaporation of solvent or the adhesion of dye molecules to the glass surface. It is expected that the parameters used for the spike identification will have an influence on the outcome of the filtering. The spike detection and removal algorithm used here is based on a simple approach that is closely related to a common method for burst selection in single-molecule studies.15,16 In that method, however, slightly more sophisticated filters, such as a Lee filter,16,17 are commonly used instead of the sliding average. The algorithm applied here has only two parameters: the averaging window size and the threshold. The influence of the threshold was investigated by varying its value from 10% to 50% of the average photon separation time in the measurement and keeping the averaging window size constant (Figure 3). For the highest threshold values, a kink appeared in the curve at lag times of 0.5-0.7 ms. For the 50% threshold, the
Figure 4. Comparison of different methods for generating correlation curves after simulated ideal spike removal. (a) Modulation filtering, (b) separate correlation of the individual remaining parts of the intensity trace and subsequent averaging, and (c) contraction of the gaps in the trace and subsequent correlation of the full contracted trace. Photons were removed for, on average, 300-µs-long time intervals separated by, on average, 100 ms (blue), 10 ms (green), and 1 ms (red) from a spike-free measurement on single-labeled liposomes (black curve).
correlation curve even dropped below 1.0 at the tail of the diffusion component. This is an effect of suboptimal spike identification and the fact that the filtering was starting to remove contributions of the free dye molecules. For comparison of the modulation filtering approach with other methods of handling data from which spikes have been removed, photon traces were taken from spike-free measurements, and photon entries were removed in time intervals with exponentially distributed widths and separations. Thereby, traces were generated that could serve as a model simulating measurements, in which spikes had been perfectly detected and removed, enabling a comparison independent of the spike identification approach. As displayed in Figure 4, three such traces from a measurement on single-labeled liposomes were used to generate
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correlation curves by three different methods. Each panel also contains the correlation curve of the unmodified measurement data for comparison. Figure 4a shows that the modulation filtering is able to perfectly regenerate the correlation curve. The curves in Figure 4b were generated by an established, commonly used algorithm,10 where a correlation curve is calculated separately for each part of the fluorescence trace between two consecutive spikes and all resulting curves are subsequently averaged. In this case, the time between spikes limits the available lag time range, and if spikes appear frequently, each trace becomes very short and a significant decrease in both the correlation amplitude and the decay time is observed. This is consistent with a previously predicted and observed bias of the correlation function for short traces.18 It should be noted that the cases presented here are relatively unusual and that this established algorithm works well in most practical cases. However, the spike frequency of the measurement presented in Figure 2 is actually almost twice as high as the lowest frequency in this example (18 Hz compared to 10 Hz), indicating that an effect of the bias cannot be excluded in all practical situations. Figure 4c shows curves generated by removing the time intervals corresponding to the spikes, thereby contracting the gaps and generating a continuous fluorescence trace, which was then correlated. Apparently, this relatively simple method works rather well and is probably a good choice in many practical cases, although it might seem inappropriate to distort the time axis. For the most extreme case, both correlation amplitude and decay time are significantly underestimated. Figure 5a shows a series of curves generated by the same gap-contraction algorithm as used for Figure 4c from the same data as shown in Figure 3. A comparison with Figure 3 shows that the curves are similar, except that the kinks that appeared before are now absent. At first glance, this might seem to be an advantage of this method over modulation filtering, but analysis of the data reveals the opposite. In Figure 5b, the χ2 parameter illustrates how well a single-diffusion-component model (eq 5) fits the data for different threshold values. For modulation filtering (black curve), threshold values of around 25%, which is the value used to generate the filtered curve in Figure 2, clearly generate the best fits. Figure 5c shows that the same threshold value also gives the best match for the diffusion time determined from the modulation-filtered data (black curve) with that of the pure sample (horizontal gray line). The trend in Figure 5c is clear: values above the gray line indicate remaining undetected spikes. Lower values are caused by distortion of the curves due to selective removal of high-intensity fluorescence signals from free dye molecules, that is, contributions of molecules taking a long path through the center of the detection volume. For modulation filtering, it seems like the goodness of fit of a properly chosen model can be used as guidance in the selection of spike identification parameters. In contrast, for the gapcontraction method, the model still fits for threshold values that are too high, although the parameters retrieved from the fit strongly diverge from the results for the pure sample. Conclusions In this study, we have presented a method to calculate an unaffected FCS curve, following proper identification of all spikes in the fluorescence intensity trace. Compared to the correlation of a photon trace or a binned intensity trace with high time resolution, the correlation of the square-wave modulation introduced by the spike removal is a very fast operation and thereby does not add much processing time, once the spikes have been marked and removed.
Persson et al.
Figure 5. Gap contraction vs modulation filtering. (a) Same data as in Figure 3, but instead of modulation filtering, the gaps in the fluorescence trace were contracted before correlation. (b) Dependence of χ2 on the threshold parameter for a fit of eq 5 to correlation curves generated, after spike removal, by modulation filtering (black) or gap contraction (red). (c) Diffusion time τD extracted from fits to correlation curves generated by modulation filtering (black) or gap contraction (red) for different threshold values. The horizontal gray line shows the diffusion time retrieved from the measurement on pure free dye.
The proposed method is generally applicable and has several potential advantages. In contrast to the common approach of separately correlating the remaining parts of the fluorescence trace after spike removal for subsequent averaging, this method makes efficient use of all available data. It keeps the time axis intact over the whole measurement and preserves correlations between data before and after removed spikes. This is especially important in cases where very intense spikes with durations shorter than the characteristic time of a process of interest occur or when spikes occur very frequently. Furthermore, the proposed modulation filtering approach makes spike removal compatible with FCS with modulated excitation.
Removal of Spikes in FCS Measurements Acknowledgment. This study was supported by funds from the Swedish Research Council (VR-NT), the European Commission 7th Framework Programme (Project FLUODIAMON, 201837), and the Royal Institute of Technology (KTH). References and Notes (1) Magde, D.; Elson, E.; Webb, W. W. Phys. ReV. Lett. 1972, 29, 705–708. (2) Rigler, R.; Elson, E. S. Fluorescence Correlation SpectroscopysTheory and Applications; Springer-Verlag: Berlin, 2001. (3) Widengren, J.; Mets, U. In Single Molecule Detection in Solution, Methods and Applications, 1st ed.; Zander, C., Enderlein, J., Keller, R. A., Eds.; Wiley-VCH Verlag Berlin Gmbh: Berlin, 2002; pp 69-120. (4) Haustein, E.; Schwille, P. Annu. ReV. Biophys. Biomol. Struct. 2007, 36, 151–169. (5) Krichevsky, O.; Bonnet, G. Rep. Prog. Phys. 2002, 65, 251–297. (6) Thompson, N. L.; Lieto, A. M.; Allen, N. W. Curr. Opin. Struct. Biol. 2002, 12, 634–641. (7) Hess, S. T.; Huang, S. H.; Heikal, A. A.; Webb, W. W. Biochemistry 2002, 41, 697–705.
J. Phys. Chem. B, Vol. 113, No. 25, 2009 8757 (8) Elson, E. L.; Magde, D. Biopolymers 1974, 13, 1–27. (9) Persson, G.; Thyberg, P.; Widengren, J. Biophys. J. 2008, 94, 977– 985. (10) Operating ManualsConfocor 3; Carl Zeiss MicroImaging GmbH: Jena, Germany, 2007. (11) Laurence, T. A.; Fore, S.; Huser, T. Opt. Lett. 2006, 31, 829–831. ¨ .; Rigler, R. J. Phys. Chem. 1995, 99, 13368– (12) Widengren, J.; Mets, U 13379. (13) Laurence, T. A.; Kwon, Y.; Yin, E.; Hollars, C. W.; Camarero, J. A.; Barsky, D. Biophys. J. 2007, 92, 2184–2198. (14) Fries, J. R.; Brand, L.; Eggeling, C.; Ko¨llner, M.; Seidel, C. A. M. J. Phys. Chem. A 1998, 102, 6601–6613. (15) Eggeling, C.; Berger, S.; Brand, L.; Fries, J. R.; Schaffer, J.; Volkmer, A.; Seidel, C. A. M. J. Biotechnol. 2001, 86, 163–180. (16) Enderlein, J.; Robbins, D.; Ambrose, W. P.; Goodwin, P. M.; Keller, R. A. Bioimaging 1997, 5, 88–98. (17) Lee, J.-S. IEEE Trans. Pattern Anal. Machine Intell. 1980, PAMI2, 165–168. (18) Saffarian, S.; Elson, E. L. Biophys. J. 2003, 84, 2030–2042.
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