Anal. Chem. 2005, 77, 36-46
Scanning Fluorescence Correlation Spectroscopy: A Tool for Probing Microsecond Dynamics of Surface-Bound Fluorescent Species Ying Xiao, Volker Buschmann, and Kenneth D. Weston*
Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306
In this report, a combined imaging and fluorescence correlation spectroscopy (FCS) method is described and its ability to characterize microsecond fluctuations in the fluorescence emission of a sample is demonstrated. A sample scanning laser confocal microscope is operated in the customary way while recording the time that each photon is detected with a time resolution of 50 ns using a low-cost counting board. The serial data stream of photon detection times allows access to fluorescence signal fluctuations that can be used to characterize dynamics using correlation methods. The same data stream is used to generate images of the sample. Using the technique, we demonstrate that it is possible to characterize the kinetics of transitions to and from nonemitting or “dark” states of the fluorescent dyes DiIC16 and ATTO 520. Results are similar to, but deviate slightly from, a model that has been frequently used for extracting singlet-triplet: conversion rates using conventional solution-based FCS. Like conventional FCS, the concentration, or in our case the areal density of coverage, of fluorescent species can also be obtained. Many single-molecule fluorescence experiments aim to extract kinetics from intensity trajectories; this method may be used as a rapid and convenient technique for characterization of surfacelinked or thin-film samples prior to performing the more time and effort intensive single-molecule measurements. Besides the capacity to measure photophysical phenomena, the surface-sensitive FCS method could also be applied for measuring conformational changes or interaction kinetics for species immobilized on a surface. One possible scenario is measurements of the frequency and duration of association of ligand-receptor pairs where a fluorescently labeled component is freely diffusing and the other is surface immobilized. Given that microarrays of custom-designed, surface-immobilized peptides and nucleic acids are now readily available, the ability to sensitively measure association and dissociation rates of the surface-linked species with a freely diffusing species could be a useful extension to what has already become an extremely important tool for characterizing the interactions of biomolecules. Fluorescence-based assays that utilize fluorescence intensity, spectrum, lifetime, or combinations of these are becoming 36 Analytical Chemistry, Vol. 77, No. 1, January 1, 2005
ubiquitous due to the extraordinary sensitivity possible with fluorescence techniques.1,2 Fluorescence methods are widely used in molecular biology, cellular, and developmental biology studies. 3 DNA microarray technology has been developed using almost exclusively fluorescence-based detection.4 Enzyme-linked immunoassays and DNA-sequencing techniques also frequently utilize fluorescence detection. Confocal fluorescence microscopy (CFM) is widely used in such assays due to the superior spatial resolution and additional sensitivity provided by out-of-plane background rejection in comparison to wide-field fluorescence microscopy.3 While dynamic processes can be time-resolved in CFM by repetitively capturing images to create movies of a sample or specimen under study, or measuring intensity transients at a single location within a sample, we demonstrate here that additional dynamic information on time scales between approximately 100 ns and 100 ms (or longer) can be obtained while imaging a sample only once. This is possible with a modification of any standard confocal microscope that uses photon-counting detectors. The modification involves the implementation of a low-cost counting board to record the time at which each photon is detected while raster scanning a sample, followed by fluctuation correlation analysis. The method is experimentally similar to the scanning fluorescence correlation spectroscopy (FCS) and image correlation spectroscopy methods initially developed in the late 1980s.5-7 However, those and more recent implementations apply the method to quantitatively characterize cluster density and cluster size in imaged samples as indicators of aggregation and heterogeneity. The method has not before been used to observe the microsecond and faster fluctuations that are caused by excitedstate processes or conformational dynamics of single molecules within a sample. Many dynamic molecular and photophysical processes are poorly understood, and the development of new methods to study * To whom correspondence should be addressed. E-mail: kweston@ chem.fsu.edu. (1) Lakowicz, J. R. Principles of Fluorescence Spectroscopy, 2nd ed.; Kluwar Academic/Plenum Publishers: New York, 1999. (2) Valeur, B., Brochon, J., Eds. New trends in fluorescence spectroscopy: applications to chemical and life science; Springer: New York, 2001. (3) Pawley, J. B., Ed. Handbook of Biological Confocal Microscopy; Plenum Press: New York, 1995. (4) Shena, M., Ed. Microarray Biochip Technology, Eaton Publishing: Natick, MA, 2000. (5) Petersen, N. O.; Johnson, D. C.; Schlesinger, M. J. Biophys. J. 1986, 49, 817-820. (6) Petersen, N. O. Biophys. J. 1986, 49, 809-815. (7) Palmer, A. G.; Thompson, N. L. Biophys. J. 1987, 51, 339-343. 10.1021/ac049010z CCC: $30.25
© 2005 American Chemical Society Published on Web 11/19/2004
them is important. Conformational changes and binding kinetics of biomolecules and the photophysics and photochemistry of UVvisible active species are routinely characterized using timeresolved methods. A wide variety of techniques have been developed to measure chemical kinetics. The fastest of these can monitor processes with characteristic evolution times of several tens of femtoseconds and longer using pulsed light sources and pump-probe methods.2 FCS is a relatively new method being used to study chemical reaction rates, molecular excited-state processes, and molecular diffusion.8-20 Most methods used to measure the kinetics of a process monitor some observable following a perturbation from equilibrium. With the exception of studies that probe excited electronic-state processes, FCS is distinct in that the sample remains at equilibrium throughout the measurement. In the FCS technique, a laser beam is focused into a sample and spatial filtering of collected light allows one to probe an extremely small sample volume. With a sufficiently small detection volume, the detected fluorescence is derived from a small number of molecules, making it possible to observe intensity fluctuations as a result of diffusion of molecules in to and out of the detection volume or fluctuations due to conformational or photophysical dynamics of those molecules. These include, for example, transitions between conformers or electronic states that differ in fluorescence brightness and fluorophore-quencher association/dissociation reactions. Fluctuations in the measured signal can only be observed when the concentration of molecules is low; at higher concentrations, the fluctuating fluorescence signals derived from individual emitters add incoherently and are lost in the noise associated with the higher detected signal level. Because of improvements in detection sensitivity and background reduction methods over the past decade, and proliferation of fluorescence-based assays, the application of FCS has increased dramatically. FCS has been utilized predominantly in free solution but has also been applied in a wide variety of other situations. These include studies of the inner compartments of cells, cell membranes, and planar biomimetic membranes.9,20-22 There are a number of advantages associated with studying samples immobilized on a flat surface in comparison to solution measurements. One of the most important advantages is the enhancement in photon collection efficiency near the glass-water or glass-air (8) Schwille, P.; Kummer, S.; Heikal, A. A.; Moerner, W. E.; Webb, W. W. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 151-156. (9) Korlach, J.; Schwille, P.; Webb, W. W.; Feigenson, G. W. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 8461-8466. (10) Magde, D.; Webb, W. W.; Elson, E. Phys. Rev. Lett. 1972, 29, 705-&. (11) Widengren, J.; Rigler, R.; Mets, U. J. Fluoresc. 1994, 4, 255-258. (12) Widengren, J.; Mets, U.; Rigler, R. J. Phys. Chem. 1995, 99, 13368-13379. (13) Edman, L.; Mets, U.; Rigler, R. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 67106715. (14) Widengren, J.; Rigler, R. Prog. Biophys. Mol. Biol. 1996, 65, PH109-PH109. (15) Widengren, J.; Rigler, R. Bioimaging 1996, 4, 149-157. (16) Widengren, J.; Dapprich, J.; Rigler, R. Chem. Phys. 1997, 216, 417-426. (17) Opitz, N.; Rothwell, P. J.; Oeke, B.; Schwille, P. S. Sens. Actuators, B 2003, 96, 460-467. (18) Kim, H. D.; Nienhaus, G. U.; Ha, T.; Orr, J. W.; Williamson, J. R.; Chu, S. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 4284-4289. (19) Hom, E. F. Y.; Verkman, A. S. Biophys. J. 2002, 83, 533-546. (20) Lieto, A. M.; Cush, R. C.; Thompson, N. L. Biophys. J. 2003, 85, 32943302. (21) Kahya, N.; Scherfeld, D.; Bacia, K.; Schwille, P. J. Struct. Biol. 2004, 147, 77-89. (22) Schwille, P. Cell Biochem. Biophys. 2001, 34, 383-408.
interface.23 The scanning FCS (sFCS) method described here has the advantage that each molecule is held in the beam for a time that is easily controlled by adjusting the linear scan rate. It is true that the time a freely diffusing molecule spends in the detection volume in standard solution FCS measurements can also be increased by enlarging the dimensions of the confocal excitationdetection volume, however, the larger confocal volume also means a higher background and, thus, lower sensitivity. Another point worth mentioning is that, in thin-film or surface-immobilized samples, fluorescent molecules are fixed in a 2-D plane that can be perfectly centered (in focus) with respect to the long axis of the elliptical confocal excitation-detection volume. In effect, the probed volume can be considered as significantly smaller than in a free solution measurement and the distribution of excitation powers within the probed volume is much narrower. This effect is substantial when considering that the ellipsoid is typically 3-5 times larger along the optical axis in comparison to the lateral axis. Other important advantages of surface immobilization are based on convenience. An individual sample (or, for example, a spot in a microarray) is easily miniaturized, which makes automated measurements on a microscope more convenient. Also, the buffer conditions can be easily exchanged by simply flowing the new buffer over the entire surface; this would be far more difficult if performing individual measurements on, for example, each well of a microtiter plate. As mentioned previously, we envision the use of the sFCS method for extracting the frequency and duration of the reversible binding of ligand-receptor pairs where one component is surface bound and the other in free solution. An example of the use of FCS to measure ligand-receptor kinetics is demonstrated in ref 20. This could be especially useful when applied to microarrays containing hundreds or thousands of surface-tethered peptides or nucleic acids, which are now widely available. Currently, peptide microarrays are used to quantify irreversible binding for enzyme profiling and mapping of protein interactions.24 DNA microarrays permit monitoring of gene expression by measuring the relative quantities of sample DNA that irreversibly hybridize to specific DNA sequences presented on the microarray. Extension of microrray-based analysis to measurements of reversible association and dissociation rates could be accomplished using sFCS when the binding event results in a change in the measured fluorescence intensity. The simplest case would be to use a fluorescently labeled, freely diffusing ligand that dwells for an extended time in the detection volume when associated with a surface-tethered binding partner (in comparison to the dwell time when no binding partner is present). The intensity fluctuation could also arise from a conformational rearrangement that affects the fluorescence quantum yield. The photophysical properties of small organic fluorescent dyes have been studied in detail for many decades. Much of the research was motivated, at least in part, by the need to optimize the performance of dye lasers.25 Other research into organic fluorophores has been aimed at development of solar cells, photodynamic therapy, biological stains, and sensors. The possibility of creating lasers that utilize dyes embedded in a solid (23) Enderlein, J. Chem. Phys. Lett. 1999, 308, 263-266. (24) Reineke, U.; Volkmer-Engert, R.; Schneider-Mergener, J. Curr. Opin. Biotechnol. 2001, 12, 59-64. (25) Drexhage, K. H. In Topics in applied physics; Scha¨fer, F. P., Ed.; SpringerVerlag: Berlin, 1973; Vol. 1, pp 144-178.
Analytical Chemistry, Vol. 77, No. 1, January 1, 2005
37
host matrix has also been explored.26 Understanding the properties and photophysical phenomena in these dyes is also important for single-molecule fluorescence spectroscopy applications. Currently, solid-state dye lasers and single-molecule fluorescence techniques are hindered by the limited photochemical lifetime of organic fluorophores. Photoinduced transitions to low quantum yield or nonemitting states, i.e., triplet states, free radicals, and isomers, limit the fluorescence rate and in some cases have been implicated as routes to photochemical destruction of dyes. Dim or dark states also cause a significant reduction in the fluorescence intensity that can be obtained from a single molecule, and this limits the precision in proposed analytical methods, such as singlemolecule DNA sequencing, that require one of several types of fluorescent dyes to be identified.27-30 Optimizing the excitation intensity and gaining in-depth understanding of photophysical processes of organic fluorophores will be benefited by new, convenient methods to measure the intermittent residence times of dim or dark states. Measurements of fluorescence intensity trajectories of isolated and immobilized single molecules have been used to characterize kinetics.18,31-37 Once a trajectory is measured, the photophysical rates have been obtained by compiling histograms of “on” and “off” times or by applying autocorrelation analysis. Since each observed molecule may have somewhat different photophysical parameters that depend on the local environment in which it resides, it is customary to collect and analyze a large number of single-molecule intensity trajectories before making any conclusions. While this is an excellent way to extract the kinetic parameters of a sample, in fact superior to all others since the full distribution of phenomena can be obtained, it is significantly more time consuming and difficult experimentally. In singlemolecule experiments, the sample concentration (areal density) must be sufficiently low that the probability of monitoring two closely neighboring fluorophores simultaneously is negligible, yet high enough that fluorescent impurities make up only a small fraction of the observed trajectories. This is a fairly restrictive sample concentration range that in practice must be optimized by trial and error. The collection of a large number of singlemolecule trajectories using confocal microscopy has been auto(26) Singh, S.; Kanetkar, V. R.; Sridhar, G.; Muthuswamy, V.; Raja, K. J. Luminesc. 2003, 101, 285-291. (27) Werner, J. H.; Cai, H.; Jett, J. H.; Reha-Krantz, L.; Keller, R. A.; Goodwin, P. M. J. Biotechnol. 2003, 102, 1-14. (28) Ambrose, W. P.; Goodwin, P. M.; Jett, J. H.; Johnson, M. E.; Martin, J. C.; Marrone, B. L.; Schecker, J. A.; Wilkerson, C. W.; Keller, R. A.; Haces, A.; Shih, P. J.; Harding, J. D. Ber. Bunsen-Gesellschaft-Phys. Chem. Chem. Phys. 1993, 97, 1535-1542. (29) Sauer, M.; Angerer, B.; Han, K. T.; Zander, C. Pccp Phys. Chem. Chem. Phys. 1999, 1, 2471-2477. (30) Neumann, M.; Herten, D. P.; Dietrich, A.; Wolfrum, J.; Sauer, M. J. Chromatogr., A 2000, 871, 299-310. (31) Ha, T.; Enderle, T.; Chemla, D. S.; Selvin, P. R.; Weiss, S. Chem. Phys. Lett. 1997, 271, 1-5. (32) Weston, K. D.; Goldner, L. S. J. Phys. Chem. B 2001, 105, 3453-3462. (33) Weston, K. D.; Carson, P. J.; Metiu, H.; Buratto, S. K. J. Chem. Phys. 1998, 109, 7474-7485. (34) Veerman, J. A.; Garcia-Parajo, M. F.; Kuipers, L.; van Hulst, N. F. Phys. Rev. Lett. 1999, 83, 2155-2158. (35) Tinnefeld, P.; Herten, D. P.; Sauer, M. J. Phys. Chem. A 2001, 105, 79898003. (36) English, D. S.; Harbron, E. J.; Barbara, P. F. J. Chem. Phys. 2001, 114, 10479-10485. (37) English, D. S.; Furube, A.; Barbara, P. F. Chem. Phys. Lett. 2000, 324, 1519.
38
Analytical Chemistry, Vol. 77, No. 1, January 1, 2005
mated in a number of laboratories.38,39 For monitoring fairly slow fluctuations, the task is facilitated by wide-field imaging methods that monitor a field of view containing many isolated single molecules simultaneously. Despite the advances in the experimental methods that are used to collect intensity trajectories, data collection and analysis is complex and time consuming and the sample preparation can be problematic given the rather specific density of coverage required for single-molecule investigations. The sFCS method described here is a relatively fast, convenient technique to measure the photophysical properties of dye molecules or other fluorescence fluctuation characteristics of a sample prior to more time-consuming single-molecule experiments. The sample preparation is far easier than that normally required for single-molecule experiments since the sample areal coverage density need only be low, but not as low as that required for singlemolecule experiments. The method can be considered as intermediate between ensemble fluorescence measurements and single-molecule methods since intensity fluctuations of single molecules are observable that cannot be observed in an ensemble measurement, yet average kinetic times are extracted since the measurement averages over many molecules. The averaging of intensity fluctuations contributed from many molecules in using the sFCS method gives results that are very similar to those that would be obtained from averaging the autocorrelation functions derived from many single-molecule intensity trajectories, as long as the fluctuations are fast compared to the time each molecule spends in the confocal detection volume (which is controlled by the scanning/imaging speed). An example in which dynamics were characterized by averaging the autocorrelation function from many single-molecule intensity trajectories was recently described.18 Several analysis methods that can be considered as alternative or supplemental to autocorrelation analysis have been devised in recent years. For example, Novikov et al. developed an analysis method using photon arrival times that allows one to extract the triplet lifetime and intersystem crossing rates.40 Fleury et al. developed the mathematical analysis needed to combine histograming analysis of measurements of the delay between photon detection events using start-stop methods with autocorrelation analysis of intensity trajectories to obtain the second-order correlation function covering delay times from 0.5 ns to 100 µs, which includes photon-antibunching and singlet-triplet interconversion dynamics.41 In addition, a plethora of other methods of analyzing fluorescence fluctuations have been invented. These include moment analysis of fluorescence-intensity distribution,7,42,43 the photon-counting histogram method,44 fluorescence intensity distribution analysis, also known as fluorescence distribution spectroscopy,45 and photon arrival time interval distribution.46 Some or all of these methods of analysis may provide information (38) Ha, T.; Chemla, D. S.; Enderle, T.; Weiss, S. Appl. Phys. Lett. 1997, 70, 782-784. (39) Sabanayagam, C. R.; Eid, J. S.; Meller, A. Appl. Phys. Lett. 2004, 84, 12161218. (40) Novikov, E.; Hofkens, J.; Cotlet, M.; Maus, M.; De Schryver, F. C.; Boens, N. Spectrochim. Acta, Part A 2001, 57, 2109-2133. (41) Fleury, L.; Segura, J. M.; Zumofen, G.; Hecht, B.; Wild, U. P. Physical Review Lett. 2000, 84, 1148-1151. (42) Qian, H.; Elson, E. L. Proc. Natl. Acad. Sci. U.S.A. 1990, 87, 5479-5483. (43) Qian, H.; Elson, E. L. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 2828-2833. (44) Chen, Y.; Muller, J. D.; So, P. T. C.; Gratton, E. Biophys. J. 1999, 77, 553567.
Figure 1. Schematic of the sample scanning laser confocal microscope adapted for sFCS. The arrival time of each detected photon is recorded with 50-ns precision using a low-cost counting board. By synchronizing photon counting with raster pattern sample scanning, images of the sample surface can be generated. The high timing precision of the photon-counting strategy allows us to generate auto- and cross-correlation curves from 50 ns to seconds.
in addition to that provided by FCS when applied to the photon detection times acquired while imaging surface immobilized or thin-film embedded fluorescent species as described in this report. EXPERIMENTAL SECTION Figure 1 shows a schematic representation of the instrument used. A cw, doubled YAG laser, λ ) 532 nm, is used for fluorescence excitation. The laser beam is directed into the back aperture of an oil immersion DIN objective (NA ) 1.25, Edmund Industrial Optics) with a dicroic beam splitter (400/535/635 TBR, Omega Optical, Inc.). The laser beam is brought to a focus 160 mm behind the back aperture of the objective so that it is tightly focused at objective working distance. Light reflected or emitted from the sample that passes through the dicroic filter is spatially filtered by a 100-µm pinhole placed in the conjugate image plane and spectrally filtered with holographic notch (Kaiser Optical Systems, Inc.) and long-pass (538 AELP, Omega Optical, Inc.) filters. Light passing though the pinhole and filters is split using a second dicroic beam splitter (570 DLRP, Omega Optical Inc.) and detected at two wavelength-selective detection channels. The pinhole is imaged 1:1 onto the active areas of two avalanche photodiode photon-counting modules (SPCM-AQR-14 PerkinElmer) using a single lens with a focal length of 100 mm placed between the pinhole and second dicroic beam splitter. The sample is mounted on a piezoelectrically driven XY scanning stage (P731K005 and PZ 62 E-500.00, Physik Instrumente) mounted above the objective. The sample stage position is controlled using an analog output PC board (National Instruments, PCI 6713). Pulses corresponding to photon detection events at the two APDs are recorded using a second PC plug-in counting board (National Instruments, PCI-6602). This board is operated in the buffered event counting mode to record the arrival time of each detected photon. An internal 20-MHz clock updates the counter value continuously; each time an electronic pulse from the SPCM arrives at the counter gate, the counter value is stored. This differs significantly from many single-molecule fluorescence acquisition (45) Kask, P.; Palo, K.; Ullmann, D.; Gall, K. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 13756-13761. (46) Laurence, T. A.; Kapanidis, A. N.; Kong, X. X.; Chemla, D. S.; Weiss, S. J. Phys. Chem. B 2004, 108, 3051-3067.
systems that typically record the number of photon counts in a user-defined integration period, typically in the range of 100 µs10 ms. Recording the arrival time of each photon with a time resolution of 50 ns allows us to produce intensity trajectories on any time scale longer than 50 ns, which can then be used to produce autocorrelation functions with that minimum time resolution. Since imaging of the sample uses the same data collection scheme, images can be displayed with an integration time per pixel as short as 50 ns along the fast-scan axis. In this paper, images are displayed with an integration time per pixel of 1 ms, which is selected to give square pixels with respect to their spatial dimension (i.e., the number of pixels displayed in the fast-scan axis is the same as the number of scan lines acquired). The analog output PC board that controls the sample X and Y positions is also used to trigger the start of fluorescence acquisition. Individual measurements consisted of scanning the sample at a constant velocity in the X axis (fast-scan axis) over 20 µm in 400 ms and back again during another 400 ms. The images presented are taken from the forward scan (trace), but an equivalent image is also produced during the retrace. The autocorrelation was calculated for each line, and these were averaged for 400 such measurements. This corresponds to 400 lines at 800 ms/line or 2 images (trace and retrace), each 400 pixels × 400 pixels with 1 ms/pixel) that are averaged to give the final scanning FCS curves. The total measurement time per image/FCS curve is 320 s. DiI samples were prepared by pipetting 10 µL of 10 nM DiI in ethanol onto a cover slide and drying in a stream of nitrogen. ATTO 520 thin-film samples were made by spin casting from a 20 mg/mL polystyrene, 10 nM ATTO 520 solution in toluene. The cover slide was spun at 2000 rpm, and 20 µL of the solution was pipetted onto the spinning slide. The sample was allowed to spin for 45 s. Data Analysis. In FCS, confocal detection is used to limit the detection region within an open volume of solution to very small dimensions. In our case, we approximate that the combined excitation and detection efficiency of our confocal microscope follows a 3-D Gaussian spatial distribution I(rb)
(
I(b) r ) I0 exp -
2(x2 + y2) ω02
-
)
2z2 z02
(1)
where ω0 and z0 are the characteristic radius and height at which the excitation-detection volume decreases by e-2 of I0. With a sufficiently low surface coverage of fluorescent molecules, a small number reside in the detection volume at any given instant. As a result, intensity fluctuations are observed as the sample is scanned across the confocal volume. In addition, intrinsic fluctuations in the emission count rate of individual molecules can be observed. In our case, the raw data measured are arrival times of each photon. These arrival times can be represented as the number of counts recorded continuously during each consecutive time bin, ∆t. This intensity trajectory can be generated with any value of ∆t g 50 ns. The normalized autocorrelation function, G(τ), is calculated from an intensity trajectory of N bins as Analytical Chemistry, Vol. 77, No. 1, January 1, 2005
39
N G(τ) )
N
N
N
t)1
t)1
t)1
∑n(t)n(t + τ) - ∑n(t)∑n(t + τ) N
N
t)1
t)1
(2)
∑n(t)∑n(t + τ) Here n(t) is the number of counts detected during the bin time with index t. In the sFCS instrument, molecules are translated along a single axis perpendicular to the optical axis. This is very similar to the observation of fluorescent species in a fluid as that fluid flows past the detection volume, assuming lateral diffusion of the molecule in the fluid is negligible. Analytical expressions have already been derived for the analysis of flow using FCS.47 These models assume that all detected species have flow in one direction with uniform velocity. Because the situation is analogous, those expressions are appropriate for sFCS. Considering only fluctuations due to translating the sample, the model equation for G(τ) is
G(τ) )
1 exp{-(τ/τscan)2} N
(3)
The term τscan can be considered as the average duration of the transit time fluorescent molecules spend in the detection volume and is determined by the width of the confocal volume at the sample surface and the scan rate used, v:
τscan ) ω0/v
(4)
The intensity fluctuations due to the act of scanning the sample and those due to intrinsic intensity fluctuations due to transitions to a dark state (e.g., a triplet state) are independent and can be treated separately as long as the intrinsic fluctuations occur on a time scale much shorter than τscan. Considering a single process that results in a dye molecule residing transiently in a dark state and assuming each detected molecule has the same rate of absorption, an exponential decay component with time constant, τds, is expected:
G(τ) )
1 D -(τ⁄τds) -(τ/τscan)2 e 1+ (e ) N 1-D
(
)
(5)
Here D is the average fraction of molecules that are in the dark state (of the N molecules in the detection volume) and τds is the characteristic bunching time that depends on the rate of transitions into and out of the dark state. The amplitude of G (at τ ) 0) decreases due to signal background that is uncorrelated. This is corrected by including the background signal, from scattering, glass fluorescence, and detector dark counts, IB, and the sum of the average fluorescence signal and the background, IS.
( ( )) ( IB IS N
1-
G(τ) ) 40
2
1+
2 D e-(τ/τds) (e-(τ/τscan) ) (6) 1-D
)
Analytical Chemistry, Vol. 77, No. 1, January 1, 2005
The excitation-dependent background signal was measured by imaging glass slides without dye applied or, when possible, by averaging the signal from regions of an image lacking emission from dyes. In the experiments described here, the conditions specified above are only approximately met. Single-molecule fluorescence measurements have been performed that demonstrate that the rate of transitions in to and out of dark states generally are distributed over a rather large range for dye molecules on dry surfaces and imbedded in thin polymer films.31,34,36,37,48-51 As for the absorption rate, since the absorption dipole orientations of the dye molecules are random along three spatial axes, some molecules are more efficiently excited than others since our laser polarization intensity is primarily in the X-Y and is at least partially linearly polarized. Regardless of whether emitted fluorescence is correlated or not, afterpulsing of the APD detector results in a decay component with a time constant of ∼1 µs with amplitude dependent on the detected count rate. We used the method described by Zhao et. al. to subtract the APD afterpulsing decay from our G(τ) data.52 The autocorrelation curves calculated from intensity data were fit to the model eq 6 using a Levenberg-Marquardt algorithm in the Labview software package. Software Calculation of G(τ). The majority of FCS and dynamic light scattering measurements are being performed using a so-called hardware correlator. These devices contain circuitry dedicated to the rapid calculation of autocorrelation and cross correlation data; the ALV-5000/FAST Tau from ALV-Laser GmbH performs 2 × 109 multiply/add operations per second. While the devices are fast, they are expensive and generally do not record the raw intensity trajectory data. In our work, we generate the FCS data from the raw photon arrival time data through software. Some effort is required to calculate an autocorrelation curve from the arrival time of each detected photon with a fast and efficient algorithm to avoid lengthy analysis times associated with large data sets. A description of our algorithm for calculating G(τ) using this method of data collection is described below. Conceptually, the simplest approach to calculate the autocorrelation component, the sum over N(t) × N(t + τ), for a data set is to generate an array, N(t) for processing. For a time resolution of 50 ns and a 1-s collection time, this requires an array of 2 × 107 time bins. For calculation of the G(τ) over 6 orders of magnitude in time, calculating this sum for each τ value in the range 50 ns-100 ms means calculating the sum 2 × 106 times (108 ns/50 ns). This would take considerable computing power and time and the linear sampling in the G(τ) data results in an unnecessarily large number of G(τ) values at longer integration times. To clearly explain this point, the number of τ samples that can be calculated between 100 ns and 1 µs with regular sampling of τ each 50 ns is 19, while the number of τ samples that can be (47) Gosch, M.; Blom, H.; Holm, J.; Heino, T.; Rigler, R. Anal. Chem. 2000, 72, 3260-3265. (48) Hubner, C. G.; Renn, A.; Renge, I.; Wild, U. P. J. Chem. Phys. 2001, 115, 9619-9622. (49) Weston, K. D.; Carson, P. J.; DeAro, J. A.; Buratto, S. K. Chem. Phys. Lett. 1999, 308, 58-64. (50) Zondervan, R.; Kulzer, F.; Orlinskii, S. B.; Orrit, M. J. Phys. Chem. A 2003, 107, 6770-6776. (51) Hou, Y. W.; Higgins, D. A. J. Phys. Chem. B 2002, 106, 10306-10315. (52) Zhao, M.; Jin, L.; Chen, B.; Ding, Y.; Ma, H.; Chen, D. Y. Appl. Opt. 2003, 42, 4031-4036.
calculated between 100 µs and 1 ms with regular sampling of τ each 50 ns is 20 000. Since we would like to observe features of the autocorrelation function for the maximum time range possible for our data (τ ) 50 ns to ∼100 ms), a nonlinear sampling of τ values allows us to reduce the number of points calculated. With our algorithm, this is done in a way that maximizes the precision of the resulting curve and minimizes the calculation time by averaging G(τ) values over progressively larger ranges of τ values at longer correlation times. Our approach to efficiently calculate G(τ) involves two different procedures, one that is most appropriately used for the short time range 50 ns to 1.5 µs and another best suited in the range 1 µs and longer. In the method used for the longer times, an array of numbers representing the number of counts (fluorescence intensity) as a function of time in constant time intervals (bins) is produced from the photon arrival time data. This is accomplished by calculating the time bin index of each photon. The time bin index, i, is the photon arrival time divided by the bin time rounded down to the nearest integer. The intensity array, A, is incremented at index i, for each photon (A(i) ) A(i) + 1). This array, A, is used to calculate the first eight values of G(τ) using the summation indicated in eq 1. With 1-µs binning, G(τ) values for τ ) 1, 2, ..., 8 µs are calculated. At this point, a new intensity trajectory array is recreated, but with the integration time per bin doubled from the previous value, so 2-µs binning. The values of G(τ) are calculated for the τ values of 10, 12, 16, and 18 µs using this array. Note that the new array could be used to calculate G(τ) for τ ) 2, 4, 6, and 8 µs, but these were already obtained from the previous array, and repeating the calculation would yield redundant G(τ) values and is not necessary. The procedure is repeated, each time rebinning the intensity trajectory with progressively larger bin times, always 2× the previous binning times, and calculating G(τ) values for τ ) 5 × j, 6 × j, 7 × j, and 8 × j, where j is the binning time of the intensity trajectory. When the number of bins in the trajectory becomes less than 200, the procedure is stopped. In general, G(τ) is calculated for continuous data sets of duration 800 ms and the iterative procedure yields 65 G(τ) values across the time range from τ ) 1 µs to τ ) 32.768 ms. The concept of increasing the sampling time along with the delay time, τ, which results in the quasi-logarithmic sampling of G(τ) was initially proposed and advanced by Sha¨tzer and is used in some, if not all, commercially available hardware correlators.53 Wohland et al. have also used a similar procedure to calculate the autocorrelation function in software.54 For calculating G(τ) values between 50 ns and 1 µs, a different approach was taken. For very short τ values, it becomes impractical to create an intensity trajectory array because of the very large length of that array. Instead, the correlation information is obtained directly from raw photon arrival time data. The time delays between detected photons are extracted and a histogram of interphoton times is created. Since the term n(t)‚n(t + τ) in eq 1 is nonzero only for the case that a photon detected at time t is followed by a photon at time t + τ, this distribution of interphoton times is equivalent to G(τ) when it is normalized properly. Interphoton times with lag times of g1 µs are ignored since these correlation times are handled in the procedure described above.
Note that the interphoton times from both consecutive and nonconsecutive photons must be included in the histogram when the probability of detecting three photons within 1 µs is not negligible. Interphoton times are calculated programmatically by simple array subtraction; the array of photon arrival times is subtracted from an identical array that is shifted in position by one or more elements. An alternate, but related method for computing the autocorrelation directly from photon arrival times was reported by Wahl et al.55
(53) Schatzel, K.; Drewel, M.; Stimac, S. J. Mod. Opt. 1988, 35, 711-718. (54) Wohland, T.; Rigler, R.; Vogel, H. Biophys. J. 2001, 80, 2987-2999.
(55) Wahl, M.; Gregor, I.; Patting, M.; Enderlein, J. Opt. Express 2003, 11, 35833591.
RESULTS AND DISCUSSION Figure 2a shows a small sample of the raw data from the photon-counting module while scanning a cover slide covered with a low areal density of Rhodamine B fluorophores. As mentioned, the raw data consist of the time of detection of each photon with a precision of 50 ns. We can think of these data instead as an intensity trajectory, where each time bin is 50 ns, as illustrated in Figure 2b. Due to the data acquisition method, no more than one photon can be detected in any one 50-ns bin at a single detector, so any 50-ns time bin will contain 0 or 1 counts but never more. The APD has a dead time of ∼60 ns, so this characteristic of the data collection method does not contribute any additional limitation or artifact in measurements. A data collection period of 1 s would require a trajectory containing 20 million 50-ns time bins to represent these data, and a calculation of G(τ) by a simple summation of products (see eq 2) would be slow and inefficient. However, using the software algorithm described and a standard PC with a 1-GHz processor, we are able to calculate G(τ) for such a data set in less than 200 ms. This makes online display of the autocorrelation curves during data acquisition possible between single line scan acquisitions. For data at higher count rates (e.g., 100 kHz), the routine becomes slower but still completes in less than 1 s. To illustrate the procedure of rebinning data for calculation of the autocorrelation function at longer times and for image display, intensity trajectories with the data rebinned with 100-µs and 1-ms time bins are shown in Figure 2c and d. The point is that the intensity trajectory shown in Figure 2c and d can be used as an intermediate data set to calculate G(τ). With longer bins, the S/N in the intensity trajectory improves, which also improves S/N in the calculated G(τ). Figure 2e shows the complete image from which the data in Figure 2a-d were taken. Note that two nearly identical images can be generated from a single data set corresponding to the forward and reverse scan motions; only the forward scan image is shown here. For the display of this and all images shown, the data are binned to 1 ms (see also Figures 3 and 5). Figure 2f shows the autocorrelation data that results from scanning this sample between 100 ns and ∼33 ms. The obvious decay at ∼4 ms is determined by the size of features in the image. Since single fluorophores are much smaller than the pixel size in these images and act as point sources of light, the feature sizes are determined solely by the axial dimensions of the combined illumination/detection volume and the linear sample scan rate. In our case, the detection volume axial width is characterized by ω0 ) 0.26 µm and the linear scan rate is 20.0 µm/300.0 ms, giving τscan ) 3.9 ms, which is in good agreement with the decay of G(τ)
Analytical Chemistry, Vol. 77, No. 1, January 1, 2005
41
Figure 2. Sample of raw image data and a demonstration of the various data processing modes used. Photon arrival times, the raw data, are shown in (a). These can be considered as intensity trajectories, i.e., counts in 50-ns bins as shown in (b), or bins any multiple of 50 ns as in (c) and (d). For display of intensity images, as in (e), 1-ms binning is used. Part f shows the resulting fluorescence correlation function also calculated from the image data from τ ) 100 ns to ∼32 ms with logarithmic spacing along the τ axis.
shown in Figure 2f. Using the amplitude of the G(τ) curve (2.0) and taking the background signal (1.1 kHz) and the average count rate across the whole image (2.65 kHz), we can determine that N, the average number of molecules in the detection volume, is 0.17. Since molecules are confined to a plane in this sample, the 42
Analytical Chemistry, Vol. 77, No. 1, January 1, 2005
detection volume can be considered instead as a detection area of πr2 ) 0.21 µm2. The total area scanned is 20 µm × 20 µm, or 400 µm2, which contains the equivalent of 1900 detection “areas”. One can then estimate the total number of molecules in the field of view to be 323. Based on visual inspection of the image, this is a bit higher than one might expect, but reasonable. Note that the alignment of excitation polarization with absorption dipole and differences in collection efficiency based on emission dipole orientation will result in a distribution of detected count rates for each molecule. Thus, many molecules are present that are not noticeable in the gray scale image. The FCS curve in Figure 2f also shows a slight decay in the time range between 1 and 100 µs. This decay component is probably real, but the amplitude is too low compared to the noise in the G(τ) curve to obtain any meaningful parameter by fitting the data to the model eq 6. Panels a and b of Figure 3 show confocal fluorescence images of a glass cover slide covered with adsorbed DiI molecules. The two images are of the same region of the same sample, but one was collected with a stream of N2 blowing onto the top of the sample. From the appearance of the images, no obvious difference is distinguished besides a decrease in the overall intensity in Figure 3b. The average count rate in Figure 3a is 25.8 kHz while in Figure 3b the average count rate is 17.3 kHz. Some of the decrease can be attributed to photobleaching of some molecules during the first scan taken in air. Despite the fact that the image data is not remarkably different for the two conditions, the autocorrelation curves shown in Figure 3c calculated from the same raw data sets used to produce these images are very obviously different. Both of the curves were fit to eq 6 (fits shown in solid lines). The autocorrelation curve calculated for the data set acquired under a nitrogen stream shows a decay component with a characteristic time of τds ) 130 µs that is nearly absent in the autocorrelation curve for the data collected in air. This component is due to fluctuating fluorescence intensity, or photon bunching, that results from intermittent residence of the molecule in a nonemitting state. Such dark states have been observed directly in single-molecule fluorescence measurements for dye molecules under equivalent conditions.31,34,36,37,48-51 These dark states have been frequently attributed to triplet states, but recent experiments performed on Rhodamine 6G provided convincing evidence that the dark state is more likely a radical ion state that is initially formed via the dye’s triplet state.50 The enhancement in the fraction of molecules in the dark state in the absence of oxygen indicates that rate of intersystem crossing out of this dark state is generally sensitive to the concentration of oxygen. By flushing the sample with pure nitrogen gas, the concentration of oxygen is reduced, and the result is that the dark-state fraction, D, becomes larger, and the characteristic G(τ) decay time, τds, due to residence in the dark state becomes longer. In air, where the concentration of O2 is high, this decay component is small because either the dark fraction is small or the characteristic time of the resulting fluctuation is
