MICROSCOPY RESEARCH AND TECHNIQUE 77:528–536 (2014)

Monitoring Triplet State Dynamics With Fluorescence Correlation Spectroscopy: Bias and Correction 1 € ANDREAS SCHONLE, * CLAAS VON MIDDENDORFF,1 CHRISTIAN RINGEMANN,1 STEFAN W. HELL,1 AND CHRISTIAN EGGELING1,2* 1

Department of NanoBiophotonics, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 G€ ottingen, Germany Present address: MRC Human Immunology Unit, Weatherall Institute of Molecular Medicine, Radcliffe Department of Molecular Medicine, University of Oxford, OX3 9DS Oxford, United Kingdom

2

KEY WORDS

fluorescence microscopy; fluorescence correlation spectroscopy; triplet; intersystem-crossing; fluorescence saturation

ABSTRACT A marker’s dark triplet state is of great importance in fluorescence microscopy: It serves as a means to switch off fluorescent markers and is thus the enabling element for several super-resolution methods. On the other hand, intersystem-crossing to the electronic dark triplet state strongly reduces the fluorescence yield in conventional fluorescence microscopy. The ability to determine the kinetic parameters of transitions into the triplet state is thus of great importance and because fluorescence correlation spectroscopy (FCS) can be applied without disturbing the system under study, it is one of the preferred methods to do so. However, conventional FCS observations of triplet dynamics suffer from bias due to the spatially inhomogeneous irradiance profile of the excitation laser. Herein, we present a novel method to correct this bias and verify it by analyzing both Monte Carlo simulated and experimental data of the organic dye Rhodamine 110 in aqueous solution for both continuous-wave and pulsed excitation. Importantly, our approach can be readily generalized to most other FCS experiments that determine intensity dependent kinetic parameters. Microsc. Res. Tech. 77:528–536, 2014. V 2014 Wiley Periodicals, Inc. C

INTRODUCTION Fluorescence microscopy is firmly established in a whole range of scientific applications. Fluorescent markers can tag molecules of interest and reveal their spatial and temporal distribution with unsurpassed specificity even in the interior of living cells (Tsien, 2003). Standard fluorescence microscopy has however two key shortcomings that call for major improvements: Its limited spatial resolution and (fluorescence) signal (Pawley, 2006). Especially in experiments where extremely high sensitivity is required, e.g., when monitoring single molecules directly (Ambrose et al., 1999; Moerner, 2007; Moerner and Orrit, 1999; Weiss, 1999; Xie and Trautmann, 1998) or using fluorescence correlation spectroscopy (FCS) (Ehrenberg and Rigler, 1974; Haustein and Schwille, 2003; Magde et al., 1972; Widengren and Rigler, 1990) the fluorescence emission within certain time span has to be maximized. To this end, usually large excitation light intensities are applied. However, this approach is limited by both, enhanced photobleaching of the fluorescent marker and depletion of the dye’s singlet system, resulting in a natural limit for the achievable fluorescence yield (Eggeling et al., 1998, 1999). Depletion of the ground state is usually not due to saturation of the transition to the excited singlet state, but rather a consequence of intersystem-crossing (ISC) to the triplet state (Kasha, 1960) and transition to other electronic dark states. With their lifetime of micro- to milliseconds (when compared with nanoseconds of the first excited singlet state), these dark states elicit periods, during which the dye is dislodged from the excitation-emission cycle which occur after a cerC V

2014 WILEY PERIODICALS, INC.

tain average number of cycles. Even if the ISCtransition probability is far below one percent as for usual single-molecule dyes such as rhodamines, this leads to accumulation in the dark states and saturation of fluorescence emission, i.e., the emitted fluorescence rate is no longer proportional to the applied irradiance but approaches a maximum beyond which it cannot be increased. Furthermore, the long-lived triplet state is an efficient precursor to photobleaching reactions such as diffusion controlled bimolecular reactions or photoreactions following the absorption of additional photons with subsequent efficient bleaching from higher excited electronic states (Anbar and Hart, 1964; Eggeling et al., 1998, 1999; Khoroshilova and Nikogosyan, 1990; Reuther et al., 1996). On the other hand, the controlled population of the long-lived dark states, such as the triplet or redox states populated thereof, is the basis for a range of optical far-field nanoscopy approaches (Bretschneider et al., 2007; F€olling et al., 2008; Hell and Kroug, 1995; Steinhauer et al., 2008; van de Linde et al., 2008), imaging tools that truly break the resolution limit of conventional *Correspondence to: Andreas Sch€onle, Department of NanoBiophotonics, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 G€ottingen, Germany. E-mail: [email protected] or Christian Eggeling, MRC Human Immunology Unit, Weatherall Institute of Molecular Medicine, University of Oxford, OX3 9DS Oxford, United Kingdom. E-mail: [email protected] Received 13 December 2013; accepted in revised form 27 March 2014 REVIEW EDITOR: Dr. Francesca Cella Zanacchi Contract grant sponsor: BMBF; Contract grant number: 0312020A; Contract grant sponsor: DFG (SFB755). DOI 10.1002/jemt.22368 Published online 11 April 2014 in Wiley Online Library (wileyonlinelibrary.com).

MONITORING DARK STATE DYNAMICS WITH FCS

fluorescence microscopy (Hell, 2007). All these methods are based on (reversibly) transferring fluorescent labels between states of different emission characteristics and electronic dark (triplet) states with long lifetimes are ideally suited. Although the ability to switch off a large fraction of the molecules inside the observation volume is mandatory, interestingly these methods still require a low ISC rate, so enough fluorescence photons are produced before switch-off (F€olling et al., 2008). Due to these specific requirements, major efforts are made to control and optimize the dark (triplet) state kinetic parameters. For example, the usage of triplet quenchers (Dittrich and Schwille, 2001; Eggeling et al., 1999; Rasnik et al., 2006; Tsien et al., 2006; Vogelsang et al., 2008; Widengren et al., 2007) may efficiently reduce triplet buildup and thus increase the maximum achievable fluorescence rate. On the other hand, specific mounting media or redox systems may supply the desired conditions for optical nanoscopy (Bretschneider et al., 2007; F€olling et al., 2008; Steinhauer et al., 2008; van de Linde et al., 2008). Additives, however, may also change the experimental environment and preclude certain applications like live-cell experiments. Dark-state relaxation (D-Rex) microscopy (Donnert et al., 2006, 2007) applies short excitation periods separated by dark periods for triplet relaxation, realized either by low repetition rate pulses (Donnert et al., 2007), bunches of quickly succeeding pulses (Donnert et al., 2007, 2009), or fast scanning microscopy (Borlinghaus, 2006; Conchello and Lichtman, 2005; Donnert et al., 2009; Moneron et al., 2010; Tsien et al., 2006; Vukojevic et al., 2008; Webb et al., 1990). However, these excitation schemes have to balance signal enhancement and imaging speed, which may either lead to low signal-to-noise ratios or long measurement times (Donnert et al., 2009). Photoinduced reverse ISC (ReISC) applies additional laser light to depopulate the triplet state (Redmond et al., 1997; Reindl and Penzkofer, 1996; Ringemann et al., 2008). However, the photoinduced depopulation involves higher excited electronic states, which are very prone to enhance photobleaching reactions, often reducing the net effect in signal improvement (Ringemann et al., 2008). Above all, dark (triplet) state kinetics of a fluorescence label may dramatically change when changing certain environmental conditions, such as the concentration and mobility of molecular oxygen (Eggeling et al., 2006; Widengren et al., 1995). Consequently, to optimize signal level and resolution in fluorescence experiments experimental procedures that can accurately characterize triplet (and dark) state dynamics under different experimental conditions without significantly perturbing the system under study are required. FCS (Ehrenberg and Rigler, 1974; Haustein and Schwille, 2003; Magde et al., 1972; Widengren and Rigler, 1990) is such a technique: by non-invasively analyzing intrinsic fluctuations in the fluorescence signal of single emitters around the thermodynamic equilibrium it can extract important molecular parameters of triplet dynamics (Widengren et al., 1994, 1995). Using FCS, the ISC and triplet decay rates of various fluorophores under different experimental conditions and when attached to biomolecules have been deterMicroscopy Research and Technique

529

mined [see for example (Eggeling et al., 1998, 2006; Ringemann et al., 2008; Steinhauer et al., 2008; Widengren and Schwille, 2000; Widengren and Seidel, 2000; Widengren et al., 1994, 1995)]. Usually these experiments are performed using a confocal microscope to define a diffraction limited observation volume, but there is an important drawback to this approach. As the triplet state is usually populated from electronically excited singlet states, the rate at which molecules leave the singlet system (the effective ISC rate) depends on the local excitation intensity and will thus vary throughout the confocal observation volume, and classical FCS analysis can only determine average values (Eggeling et al., 1998; Ringemann et al., 2008; Widengren et al., 1994, 1995). Especially in case of saturated excitation, i.e., for increasingly depleted ground states, this averaging introduces a systematic bias because saturation effects affect the focal center, i.e., the spot of highest irradiance, much more than the focal periphery (Ringemann et al., 2008). Herein, we present a novel analysis method that takes into account the spatial variation of the excitation rate. Our analysis approach efficiently corrects for bias introduced by conventional focal averaging, requiring only a prior knowledge of the experimental parameters. Using Monte Carlo simulated and experimental data of the organic dye Rhodamine 110 (Rh110) in aqueous solution, we demonstrate both, how the bias of conventional analysis affects experimental results, and that our method is able to avoid this bias. Importantly, the bias of the conventional FCS analysis is much more severe when using pulsed excitation as opposed to continuous-wave excitation. In both cases, our analysis allows for a completely bias-free determination of triplet parameters from FCS data. EXPERIMENTAL SECTION Sample Preparation All samples were freshly prepared and measured at room temperature of  22 C. We diluted the dye Rhodamine110 (Rh110) (Lambda Physik, G€ottingen, Germany) in PBS buffer pH 7. The final dye concentration was approximately 1029 M for FCS measurements. We performed measurements of the free diffusing dyes in 100 mL samples sealed on microscope cover glass. Spectroscopic parameters of the dye Rh110 in water were absorption cross-section rexc 5 2.6 3 10216 cm2 at 488 nm as determined by an UV-Vis spectrometer (Cary 4000, Varian, Darmstadt, Germany) and a fluorescence lifetime of 1/sF 1/k10 5 4 ns as measured by timecorrelated single-photon counting [pulsed excitation at 488 nm (PicoTA, Picoquant, Berlin, Germany) and signal registration by a PC card (SPC 830, Becker & Hickl GmbH, Berlin, Germany)]. Confocal Microscope The FCS measurements were performed at a confocal epi-illuminated microscope described in detail previously (Ringemann et al., 2008). In brief, the main parts were a microscope body (DM IRB, Leica Microsystems, Mannheim, Germany) equipped with a water immersion objective (60 3 UPLSAPO, NA 1.2, Olympus, Japan) and a linear-polarized excitation laser at 488 nm either delivering continuous-wave (Argon

530

€ A. SCHONLE ET AL.

Fig. 1. Triplet kinetics of a conventional fluorophore. a: Electronic three-state diagram with electronic ground S0 and first excited singlet state S1, and lowest excited triplet state T and interconversion rates. For details see text. b: Simplification to a two-level system including the singlet entity {S0,S1} and the triplet T with interconversion rates kTS and the effective ISC rate kISC , which depends on irradiance I and thus on space r.

laser, Innova 70C, Coherent, CA) or pulsed (PicoTA, Picoquant, Berlin, Germany,  80 ps pulse width and 80 MHz repetition rate) laser light. Coupling into the microscope was accomplished by appropriate dichroic mirrors (AHF Analysentechnik, T€ ubingen, Germany). We spatially and spectrally filtered and 50:50 split up the fluorescence emission from the focal laser spot by the confocal pinhole and by bandpass filters (AHF Analysentechnik) before detection by two single-photon avalanche photodiodes (SPCM-AQR-13-FC, Perkin Elmer Optoelectronics, Fremont, CA). We further analyzed the single-photon counting detection events using a hardware correlator card (Flex02-01D, Correlator.com, NJ). We determined the size of the excitation volume from correlation data of Rh110 diffusion at low excitation irradiances (with the known diffusion constant D 5 3 3 1026 cm2 s21 of Rh110 in water). The 1/e2-radius x0 of the focal spot together with the measured laser power P at the sample allowed us to calculate the applied irradiance I5P=ðp=2x20 Þ. Experimental parameters of the setup were the 1/e2-radius x0  300 nm of the 488 nm light, a numerical aperture NAobj 5 1.2 of the objective lens, numerical apertures NAexc  NAem  NAobj for laser focusing (diameter of the collimated laser beam dlaser  dobj diameter of the back aperture of the objective) and for collecting the emitted fluorescence, respectively, the microscope’s image magnification M 5 100, and a diameter dconf 5 62.5 mm of the confocal pinhole. All measurements were recorded at room temperature and fitting of data were done using customwritten software (C and LabView). Monte Carlo Simulation We used Monte Carlo simulations to generate fluorescence time traces of single fluorophores diffusing through a three-dimensional Gaussian-like focal spot area, undergoing triplet transitions. The fluorophores were assumed to diffuse freely in three dimensions with parameters as close as possible to our experiments. Initially, 100 molecules were distributed randomly on a simulation support area of 1 mm 3 1 mm.

The simulations featured stochastically stable results after 5 3 107 time steps of 0.1 ms length using a focal maximum brightness of 1,000 MHz. The symmetrically normalized auto-correlation curves of the fluorescence time traces were numerically calculated using the multi-tau correlation method (Sch€ atzel et al., 1988). Input parameters to the simulations were a diffusion constant D 5 3 3 1026 cm2 s21, an inverse rate constant of S1!S0 de-excitation 1/k10 5 4 ns, an ISC rate kISC 5 1 ms21, a triplet de-excitation rate kT 5 0.2 ms21, and an absorption cross-section rexc 5 2.6 3 10216 cm2. For pulsed excitation we used pulse lengths of Tp 5 80 ps at a repetition rate of 1/Tr 5 80 MHz. The focal spot and the collection efficiency function of the microscope were calculated with Richard/Wolf diffraction theory (Richards and Wolf, 1959) applying wavelengths of 488 nm for excitation, 515 nm for detection, a pinhole diameter of d 5 20 mm, a microscope magnification of M 5 35, and a numerical aperture NAexc 5 NAem 5 NAobj 5 1.2. RESULTS Triplet Kinetics Figure 1a shows a simplified energy level diagram of a fluorophore and the most important transitions with electronic ground and first excited singlet states S0 and S1, respectively, and lowest excited triplet state T. Following excitation to S1, the fluorophore can either relax back to S0 by internal conversion or by emission of a photon (with quantum yield UF) or cross to T (ISC). From T, the fluorophore relaxes back to S0. Herein, we have disregarded vibrational sub-levels and excitation to higher excited electronic singlet and triplet states. The rate constants kexc for S0!S1 excitation, k10 for S1! S0 de-excitation, kISC for S1!T crossing, and kTS for T! S0 decay define the rate system of the time t dependent relative populations of the different states [Eq. (1)]. 0 1 0 1 S0 ðtÞ 2kexc C B C dB B C B C B S1 ðtÞ C5B kexc CS0 ðtÞ A @ A dt @ TðtÞ 0 0 1 0 1 (1) k10 kTS B C B C B C B C 1B 2k10 2kISC CS1 ðtÞ1B 0 CTðtÞ @ A @ A 2kTS kISC S0(t), S1(t), and T(t) express the relative probabilities of a fluorophore to be in the respective electronic state after time t, with S0(t) 1 S1(t) 1 T(t) 5 1 and S0(0) 5 1. The rate constant kexc 5 rexc c I for excitation is given by the absorption cross-sections rexc at the excitation wavelength, the reciprocal photon energy c of the excitation light, and the excitation irradiance I. Following continuous or quasi-continuous excitation, the electronic levels reach equilibrium with the respective steady-state populations S0eq, S1eq, and Teq of the singlet ground state S0, the singlet excited state S1, and the lowest excited triplet state T (Eggeling et al., 1998; Ringemann et al., 2008; Widengren et al., 1995) [Eq. (2)]. Microscopy Research and Technique

MONITORING DARK STATE DYNAMICS WITH FCS

S1eq 5

kexc kTS kTS ðkexc 1k10 Þ1kISC ðkTS 1kexc Þ

kISC k10 Teq 5 S1eq S0eq 5 S1eq kTS kexc

531

(2)

The kinetics of the singlet state system (k10) is usually much faster than the triplet transitions rate constants: k10 >> kISC, kTS (Eggeling et al., 1998; Ringemann et al., 2008; Widengren and Seidel, 2000; Widengren et al., 1995). This characteristic allows the simplification to a two-state model comprising the S0– S1 singlet system and the triplet state T with respective interconversion rate constants kISC and kTS (Fig. 1b) [Eq. (3)]. ! ! ! 2kISC kTS d SðtÞ SðtÞ1 TðtÞ (3) 5 dt TðtÞ kISC 2kTS with kISC 5pS1 kISC and pS1 5 kexckexc 1k10 Herein, we have introduced an effective ISC rate kISC that depends on the excitation irradiance (via kexc) and includes the saturation characteristics of the S0–S1 system with pS1 denoting the probability of populating the first excited state S1 within the singlet system. With S(0) 5 1 and T(0) 5 0, the time-dependent population of the singlet entity S(t) as well as the steady-state populations of the singlet entity Seq and of the triplet Teq are given by:   SðtÞ5Seq 1Teq exp 2ðkISC 1kTS Þt (4) k

ISC with Seq 5 k kTS 1kTS and Teq 5 kISC 1kTS ISC As expected, Eqs. (2) reduce to (4) for k10 >> kISC. With increasing excitation irradiance I and, thus, increasing excitation rate kexc, the steady state populations of triplet and first excited singlet state increase and, consequently, so does the effective ISC rate kISC , but all saturate due to depletion of the ground state (Fig. 2a).

FCS FCS analyses characteristic fluctuations dF(t) in the fluorescence signal F(t) in time t about an average value F(t) 5 1 dF(t) by calculating the secondorder auto-correlation function G(tc) (Ehrenberg and Rigler, 1974; Haustein and Schwille, 2003; Magde et al., 1972; Widengren and Rigler, 1990) [Eq. (5)]. Gðtc Þ511

hdFðtÞdFðt1tc Þi hFðtÞi2

correlation function taking diffusion dynamics and dark triplet state population into account can be approximated by Eq. (6) (Ringemann et al., 2008; Widengren et al., 1995). Gðtc Þ511 with GD ðtc Þ5

(5)

Herein, tc represents the correlation time. Triangular brackets indicate averaging over the measurement time t. The overall fluorescence signal F(t) detected from a solution of fluorescent molecules is given by the number N(t) of molecules in the observation volume and the fluorescence brightness (or detected count rate per time unit) q of each single molecule. Characteristic variations in N(t) are for example caused by diffusion of a dye molecule in and out of the confocal detection volume, and in q(t) by transition into and out of the dark triplet state. Following earlier work, the autoMicroscopy Research and Technique

Fig. 2. a: Depletion of the steady-state population of the singlet ground state S0eq, saturation of the steady-state populations of the excited singlet S1eq and triplet states Teq and saturation of the effective ISC rate kISC , calculated using Eq. (4) and parameters 1/k10 5 4 ns, kISC 5 1 ms21, kTS 5 0.2 ms21, and rexc 5 2.6 3 10216 cm2 at 488 nm. b: Spatial dependence of the effective ISC rate kISC ðrÞ (black line) for a Gaussian-assumed irradiance distribution I(r) (grey dotted line) for two laser powers P 5 100 mW (upper panel) and 1 mW (lower panel). At high laser powers saturation of S1 leads to a distortion of kISC ðrÞ from the Gaussian to a more square-like profile, which results in an underestimation of values of an average kISC ðIav Þ (black rectangle).



1 11tc =sD

T GT ðtc Þ511 12Teqeq

1 ½GD ðtc ÞGT ðtc Þ



1=2

1 11ðx0 =xz Þ2 ðtc =sD Þ

(6)

(diffusion) and

exp ð2tc =sT Þ (triplet) Herein, a spatial three-dimensional Gaussian profile ð exp ð22ðx2 =x20 1y2 =x20 1z2 =x2z ÞÞ with spatial coordinates r 5 (x, y, z)) of the detected fluorescence is used to approximate the confocal detection volume. The characteristic diffusion time sD 5x20 =ð4DÞ is then given by the diffusion constant D and the 1/e2 radius x0 of the profile, and x0/xz describes the ratio of lateral to axial 1/e2 radii. The parameter Teq depicts the steady-state triplet population as expressed in Eq. (4), while the triplet correlation time sT 51=ðkISC 1kTS Þ is given by the effective ISC and the triplet de-excitation rates kISC and kTS, respectively. The triplet correlation function

€ A. SCHONLE ET AL.

532

GT(tc) follows from the relative fluctuations of the singlet system due to the triplet transitions given by Eq. (4): SðtÞ=Seq 511Teq =ð12Teq Þ exp ½-ðkISC 1kTS Þt. Important assumptions of this model are (i) a diffusion constant D that is unaffected by an electronic state change, (ii) no fluorescence is detected from a molecule in the triplet system, and (iii) constant rates kISC and kTS over the irradiation volume. Conditions (i) and (ii) are fulfilled for most fluorophores but condition (iii) assumes a homogeneous irradiation with excitation light throughout the detection volume. The Problem: Inhomogeneous Irradiance Profile and Saturation However, FCS is usually applied with inhomogeneous spatial profiles of the excitation irradiance. For example, in its most frequent application in a confocal microscope, the exciting laser light is strongly focused by a high-numerical aperture objective lens, producing an irradiance profile I(r) that is well approximated by a Gaussian Iðx; yÞ  I0 exp ð22ðx2 =x20 1y2 x20 Þ in the focal plane (Pawley, 2006). For proper analysis of FCS, one needs to know the exact shape of the detected fluorescence, i.e., the spatial brightness profile q(r). Different parameters determine q(r): the irradiance profile I(r), which establishes the fluorescence excitation profile, i.e., the spatial probability distribution of the first excited singlet state population S1eq(I(r)) [compare Eq. (4)], and the collection efficiency function CEF(r) given by the detection profile of the imaging system (i.e., the point-spread function of the microscope objective and the transmission function of the confocal pinhole) [Eq. (7)]. qðrÞ5KS1eq ðIðrÞÞCEF ðrÞ

(7)

Herein, the constant K 5 UDet UF k10 includes the detection efficiency UDet of the setup, the fluorescence quantum yield UF, and the S1! S0 de-excitation rate k10. For analyzing the molecular diffusion through the confocal laser spot, q(r) is usually approximated by a Gaussian distribution, resulting in a diffusion term GD(tc) as given in Eq. (6). This is valid for low excitation irradiances, were the brightness (or population S1eq) linearly follows the excitation irradiance, but leads to significant distortions when the first excited singlet state population and thus the fluorescence yield starts to saturate, i.e., it is no longer proportional to the excitation irradiance (compare Fig. 2a). This saturation effect mainly affects the focal center, i.e., the point of highest irradiance and results in a distorted, more square-like brightness profile q(r). Conventional FCS analysis consequently determines biased values of diffusion coefficients. Although this issue has been dealt with in detail previously (Enderlein et al., 2005) and solved by, for example, measuring diffusion on a dual-focus FCS setup that is insensitive to saturation effects (Dertinger et al., 2007), we are here not interested in diffusion coefficients but in the proper determination of triplet kinetic parameters and leave the diffusion problematic untouched. When determining ISC rate constants with FCS, one also has to regard the spatial profile of I(r), as this results in a spatial inhomogeneity of the effective ISC

rate kISC ðIðrÞÞ and thus of the steady-state triplet population Teq(r) (Fig. 2b). In previous evaluations, this issue has been solved by assuming an average irradiance Iav 5 I0/2 (with I0 denoting the peak focal irradiance) and thus average effective ISC rate kISC ðIav Þ and triplet population Teq 5 Teq(Iav) over the whole excitation volume (Eggeling et al., 1998, 2005; Ringemann et al., 2008; Widengren et al., 1994). From the values of Teq and sT determined by fitting Eq. (6) to FCS data one can deduce the ISC and triplet de-excitation rate constants kISC and kTS, respectively (Eggeling et al., 1998, 2005; Ringemann et al., 2008; Widengren et al., 1994) [Eq. (8)]. kISC 5

  1 k10 Teq 11 kexc ðIav Þ sT

1 kTS 5 ð12Teq Þ sT

(8)

The only a priori knowledge needed is the absorption cross-section rexc, the peak focal irradiance I0, and the S1!S0 de-excitation rate constant k10, which can all be determined by independent measurements: rexc from the absorption spectrum, I0 5 P/Aexc from the laser power P measured at the sample and the focal area Aexc  p=2x20 , and k10  1/sF from the fluorescence lifetime sF, e.g., measured by time-correlated singlephoton counting. It has been shown that this approximation gives a very good estimate of kISC and kTS for Gaussian-like profiles and moderate saturation of fluorescence emission, i.e., for low excitation irradiances (Eggeling et al., 1998, 2005; Ringemann et al., 2008; Widengren et al., 1994). At high irradiances, saturation of S1 leads to a severe distortion of kISC ðrÞ from a more Gaussian-like to a more square-like profile (Fig. 2b), biasing the approximation via an average kISC ðIav Þ and thus resulting in obviously wrong values of kISC at large I (Ringemann et al., 2008). Figure 3 exemplifies this problem for simulated as well as for experimental data of continuous-wave (cw) excitation. We used Monte Carlo simulations to generate correlation data of single fluorophores diffusing through a tightly focused laser spot and detected by a confocal setup. The experimental conditions were assumed similar to those of our confocal microscope. The data generated for different laser powers P were fit by Eq. (6) and values of kISC and kTS determined according to Eq. (8) and the above averaging approach kISC 5kISC ðIav Þ. Although the determined values of kTS match the input value of kTS 5 2 3 105 s21 for all P and are thus not biased, values of kISC are underestimated, especially for large P. A true value can only be resolved by interpolation to low laser powers (Ringemann et al., 2008). Experimental data of the dye Rhodamine 110 (Rh110) in aqueous solution gives similar characteristics when the averaging approach is applied, with slight differences in kTS. The differences result from reverse intersystem-crossing (ReISC), where the excitation laser depopulates the triplet state via higher excited electronic states. As a consequence, kTS increases from  2 3 105 s21 at low laser powers to  4 3 105 s21 at P > MW cm22, as in detail outlined previously (Ringemann et al., 2008). The increase in kTS Microscopy Research and Technique

MONITORING DARK STATE DYNAMICS WITH FCS

Fig. 3. FCS analysis of triplet kinetics following cw irradiation: simulated and experimental data of Rh110 in water. a,b: Exemplary correlation curves (a: simulated, b: experimental) show an increasing decay in the ms time range with increasing laser power P, indicating the enhanced population of the triplet state. Eq. (6) fits all data well. c,d: Values of kISC (black circles) and kTS (grey squares) determined from the simulated (c) and experimental data (d) using the conventional averaging analysis (([Eq. (8)], open symbols k(av)) and applying our bias-free analysis approach ([Eq. (12)], closed symbols k(n)). The dotted lines in (c) depict the input values of the simulation. Error of experimental data 8%.

thus results from a true photophysical phenomenon and is not a consequence of ground state depletion as for values determined for kISC. The latter strongly decreases with increasing P, and a value of kISC  6–7 3 105 s21 can indeed only be approximated for low P. These observations are in line with previous FCS triplet measurements (Eggeling et al., 1998, 2005; Ringemann et al., 2008). Correction of Saturation Effects A first approach to correct for the bias in values of kISC introduced by saturation was obtained by Widengren et al. (1995). Values of kISC and kTS of different organic dyes were determined by globally fitting a series of values of Teq and sT extracted from correlation data recorded at a whole set of different excitation irradiances. The fit uses volume integrals to spatially average over the inhomogeneity Teq(r), assuming a Microscopy Research and Technique

533

Gaussian irradiance distribution. Besides the need to record a whole set of correlation data at different laser powers, a somehow inaccurate description of the experimental data became obvious for fluorophores with large ISC yields such as Fluoresceine. Herein, we apply a somehow different approach, allowing us to accurately determine values of kISC and kTS from correlation data recorded at a single irradiance only, not demanding the recording of a whole set of data at different laser powers. Furthermore, it realizes a straightforward introduction of an accurate and flexible description of any irradiance profile as well as of other setup parameters such as the collection efficiency function. We introduce the spatial dependence of the rate constant kISC ðrÞ into our model by using the following simple consideration. Imagine different fluorescing molecules i with brightness qi in the sample with their respective correlation curve Gi(tc) 5 GD,i(tc) GT,i(tc) given by Eq. (6). In this case, the measured correlation P 2 P curve is Gðtc Þ5 i q2i GD;i ðtc ÞGT;i ðtc Þ= i qi . Since the diffusion time sD is much larger than the triplet correlation time sT(r 5 0) at the focal center, the molecules can be considered quasi-stationary in the time regime of triplet dynamics and we can treat the two correlation functions separately: (G(tc) 5 1 1 1/ GD(tc) GT(tc) with GD(tc) given by Eq. (6) and P 2 P GT ðtc Þ5 i q2i GT;i ðtc Þ= i qi ). In addition, for calculating the contribution GT(tc) of the triplet fluctuations to the correlation function, let us treat molecules at different positions as different kind of molecules. With Teq(r) and sT 51=ðkISC ðrÞ1kTS Þ introduced in Eq. (4), we can therefore write an exact expression of GT(tc):

 ð Teq ðrÞ GT ðtc Þ5C2 q2 ðrÞ 11 exp ð2tc =sT ðrÞÞ d3 r (9) 12Teq ðrÞ with qðrÞ5KS1eq ðrÞCEFðrÞ5KS eq ðrÞpS1 ðrÞCEFðrÞ Ð The factor C 5 1/ q(r) d3r is the inverse volume integral over q(r) normalizing GT(tc) to Eq. (6) for spaceinvariant rates. Although we could use this result directly to model our data, it is advantageous to rewrite Eq. (9) in the form: ð GT ðtc Þ5C2 mð2Þ ðxÞSeq ðxI0 Þ2 pS1 ðxI0 Þ2

 (10) Teq ðxI0 Þ exp ð2tc =sT ðrÞÞ dx 11 12Teq ðxI0 Þ Ð with mðjÞ ðxÞ5 dðIðrÞ=I0 2xÞðCEFðrÞÞj d3 r The factor m(j)(x) only determines the collection efficiency function CEF(r) and the form of the excitation pattern and is independent of any other parameter. It can therefore be pre-calculated before fitting, reducing the numerical effort from a three- to a one-dimensional integral. For the calculation of the integrals, the actual shape of I(r) is of no importance, but it requires only the knowledge of the relative volume size that a value of I(r) 5 xI0 spans. This reduction is similar to an approach used for fitting photon count histograms (Kask et al., 1999) and is here realized by the d-function, which equals 1 only if I(r) 5 xI0. Consequently, we can simplify the volume integral over q(r):

€ A. SCHONLE ET AL.

534

ð

ð qðrÞd3 r5K mð1Þ ðxÞSeq ðxI0 ÞpS1 ðxI0 Þdx

(11)

The final fitting function then takes the form of Eq. (12) Gðtc Þ511Gð0Þ½GD ðtc ÞGT ðtc Þ

(12)



C with Gð0Þ5 in which the diffusion correlation term GD(tc) is given by Eq. (6), the triplet correlation term GT(tc) by Eq. (10), the average particle number was defined in Eq. (6) and the normalization factor C* is introduced so that Eq. (12) reduces properly to Eq. (6) for the case of a constant rate kISC ðrÞ: Ð ð1Þ m ðxÞpS1 ðxI0 Þdx  C 5 Ð Ð 2 ð2Þ ½ m ðxÞpS1 ðxI0 Þ dx½ mð1Þ ðxÞSeq ðxI0 ÞpS1 ðxI0 Þdx2

(13) Note that, in our case, we do not demand exact knowledge of C*, as we are not interested in a determination of the average particle number. Free parameters to our fitting function [Eq. (12)] are the amplitude G(0), the diffusion time sD, and the rate constants kISC and kTS. We pre-determine and fix values of the axis ratio x0/xz from control measurements on a single dye solution at very low I, of the absorption cross-section rexc, the peak focal irradiance I0 and the S1!S0 de-excitation rate constant k10 as outlined above [Eq. (8)], of the numerical aperture NAexc for laser focusing, of the numerical aperture NAem for collecting the emitted fluorescence, of the microscope’s image magnification M and of the diameter dconf of the confocal pinhole. The values of I0, NAexc, NAem, M, and dconf are input to calculating I(r) and CEF(r) (Richards and Wolf, 1959). Although the numerical aperture NAem 5 NAobj for collecting fluorescence is simply given by the numerical aperture NAobj of the objective lens, the diameter dlaser of the collimated laser beam with respect to the diameter dobj of the back aperture of the objective determines NAexc, and NAexc 5 NAobj only for dlaser  dobj, otherwise NAexc < NAobj. Fitting our revised model [Eq. (12)] to the Monte Carlo simulated as well as to the Rh110 experimental correlation data results in significantly improved values of kISC, which now do not decrease but render almost consistent results at any P (Fig. 3). Furthermore, values of kTS are roughly the same as those determined by our averaging approach [Eq. (8)] (note the confirmation of the increase in kTS due to optically driven ReISC). In the case of the simulated data, the results confirm the input parameters (Fig. 3c). Fluctuations in the experimental data (especially of kISC) result from the uncertainty of determining the irradiance values I0, but lie within the 8% uncertainty as given by the standard deviation from repeated measurements. Including the spatial saturation characteristics into the fitting model consequently allows an accurate determination of triplet parameters at any excitation power. Pulsed Excitation Depletion of the singlet ground state and thus saturation of the S0!S1 transition is more pronounced for

pulsed excitation (Gregor et al., 2005). Although excitation with large repetition rates in the range of 80 MHz can in principle be regarded quasi-continuous (Eggeling et al., 2005), differences in the saturation behavior of continuous (cw) and quasi-continuous wave (quasi-cw) excitation arise (Eggeling et al., 2005; Gregor et al., 2005). For cw excitation, a single fluorophore is permanently absorbing. In the case of pulsed excitation, absorption occurs only during a fraction of time, i.e., during the pulse. This disadvantage is not compensated by the enhanced peak irradiance, as a fluorophore can only be excited once per pulse (a pulse width of usually 0.1–100 ps is much shorter than the typical lifetime of 2–4 ns of a fluorophore). The difference in saturation characteristic between cw and quasi-cw excitation grows with decreasing pulse width and/or decreasing repetition rate (Gregor et al., 2005). For example, it has been shown that the maximum fluorescence brightness of Rhodamine 6G in aqueous environment is approximately 1.5-times lower for 80 MHz excitation with  100 ps long pulses than for cw excitation (Eggeling et al., 2005). The increased pulse saturation effect becomes obvious in the conventional FCS analysis of simulated and experimental (Rh110 in aqueous solution) correlation data recorded for pulsed excitation with 80 MHz repetition rate and  80 ps pulse width (Fig. 4). Although values of kTS are again accurately recovered for any averaged power P (note again the increase in experimentally determined values of kTS due to optically driven ReISC), the values of kISC resulting from the averaging approach [Eq. (8)] are severely biased for large P. The decrease below the correct value is much more pronounced for pulsed excitation than for the cw data (compare Fig. 3), making a correction approach even more essential. In principle, we can apply the same correction procedure as outlined above in Eqs. (9) to (13). The only difference is that we have to regard the increased pulse saturation in the S0!S1 excitation process. Herein, we can follow an approach given by Gregor et al. (2005), and simply replace the probability pS1 of populating the first excited state S1 within the S0–S1 singlet system [Eq. (3)] by an expression regarding the repetitive excitation with rectangular pulses of length TP and repetition rate 1/Tr:

2 kexc ðrÞ TP kexc ðrÞ pS1 ðrÞ5 1 kexc ðrÞ1k10 Tr kexc ðrÞ1k10 (14)  2k ðT 2T Þ  2ðk 1k ÞT  r exc 10 10 P P 21 e 21 e ½k10 Tr ½12e2ðk10 Tr 1kexc TP Þ  The modification of Eq. (12) using this expression, and the fitting of this modified model to the simulated and experimental data resulted in the complete correction of the bias. No decrease in kISC is observed and the input parameters of the simulation are well recovered by our corrected analysis (Fig. 4). Fluctuations in the experimental data (especially of kISC) result from the uncertainty of determining the irradiance values I0, but lie within the 8% uncertainty as given by the standard deviation from repeated measurements. Even for pulsed excitation with an enhanced saturation behavior, our corrected FCS analysis delivers Microscopy Research and Technique

MONITORING DARK STATE DYNAMICS WITH FCS

535

rately be observed in different environments (such as different pH or different concentration of molecular oxygen, or different labeling conditions). This may be crucial, as the triplet kinetics are extremely sensitive to the fluorophore’s environment. We are confident that our improved FCS analysis will be helpful in optimizing fluorescence experiments in all kinds of scientific areas. For example buffer conditions or fluorophores may be inspected, to reduce the triplet yield as much as possible, to maximize fluorescence emission, and to optimize experimental conditions for far-field nanoscopy based on optical dark-state transfer (or ground-state depletion). Our approach is not limited to the determination of triplet or other dark state kinetic parameters but is generally favorable for the determination of irradiance dependent kinetic parameters such as photobleaching kinetics, cis-trans photoisomerization, or photochemical processes. REFERENCES

Fig. 4. FCS analysis of triplet kinetics following pulsed irradiation: simulated (a) and experimental data of Rh110 in water (b). Values of kISC (black circles) and kST (grey rectangles) using the conventional averaging analysis ([Eq. (8)], open symbols k(av)) and applying our bias-free analysis approach ([Eq. (12)], closed symbols k(n)). The dotted lines in (a) depict the input values of the simulation. Error of experimental data 8%.

accurate results of the triplet parameters for any average excitation power. DISCUSSION We have presented a novel and bias-free approach to determine ISC parameters of fluorescent dyes with FCS. We take into account the spatial dependence of the irradiance and thus of the effective ISC rate, and realize an accurate consideration of spatial inhomogeneities introduced by the depletion of the fluorophore’s ground (or saturation of the excited fluorescent) state at large excitation irradiances. Ground state depletion (or saturation of fluorescence) is crucial in experiments determining the kinetic parameters of long-lived dark states such as the triplet state, since these experiments inherently have to apply large excitation irradiances to induce a significant dark state population. Our modified FCS analysis may determine triplet kinetic parameters from correlation data recorded at a single irradiance only, not demanding the recording of a whole set of data at different laser powers. In addition, our analysis allows the consideration of any irradiance profile or of different setup parameters such as different magnifications or numerical apertures of the microscope objective or different pinhole sizes of the confocal detection. Input parameters to our analysis can easily be determined a priori. Using FCS and our modified analysis model, triplet parameters can accuMicroscopy Research and Technique

Ambrose WP, Goodwin PM, Jett JH, vanOrden A, Werner JH, Keller RA. 1999. Single molecule fluorescence spectroscopy at ambient temperature. Chem Rev 99:2929–2957. Anbar M, Hart EJ. 1964. Reactivity of aromatic compounds toward hydrated electrons. J Am Chem Soc 86:5633–5637. Borlinghaus RT. 2006. Mrt letter: High speed scanning has the potential to increase fluorescence yield and to reduce photobleaching. Microsc Res Tech 69:689–692. Bretschneider S, Eggeling C, Hell SW. 2007. Breaking the diffraction barrier in fluorescence microscopy by optical shelving. Phys Rev Lett 98:218103. Conchello J-A, Lichtman JW. 2005. Optical sectioning microscopy. Nat Method 2:920–931. Dertinger T, Pacheco V, von der Hocht I, Hartmann R, Gregor I, Enderlein J. 2007. Two-focus fluorescence correlation spectroscopy: A new tool for accurate and absolute diffusion measurements. ChemPhysChem 8:433–443. Dittrich PS, Schwille P. 2001. Photobleaching and stabilization of fluorophores used for single-molecule analysis with one- and twophoton excitation. Appl Phys B 73:829–837. Donnert G, Keller J, Medda R, Andrei MA, Rizzoli SO, Lurmann R, Jahn R, Eggeling C, Hell SW. 2006. Macromolecular-scale resolution in biological fluorescence microscopy. Proc Natl Acad Sci USA 103:11440–11445. Donnert G, Eggeling C, Hell SW. 2007. Major signal increase in fluorescence microscopy through dark-state relaxation. Nat Method 4:81–86. Donnert G, Eggeling C, Hell SW. 2009. Triplet-relaxation microscopy with bunched pulsed excitation. Photochem Photobiol 8:481–485. Eggeling C, Widengren J, Rigler R, Seidel CAM. 1998. Photobleaching of fluorescent dyes under conditions used for single-molecule detection: Evidence of two-step photolysis. Anal Chem 70:2651–2659. Eggeling C, Widengren J, Rigler R, Seidel CAM. 1999. Photostabilities of fluorescent dyes for single-molecule spectroscopy: Mechanisms and experimental methods for estimating photobleaching in aqueous solution. In: Rettig W, Strehmel B, Schrader M, Seifert H, editors. Applied fluorescence in chemistry, biology and medicine. Berlin: Springer. pp. 193–240. Eggeling C, Volkmer A, Seidel CAM. 2005. Molecular photobleaching kinetics of rhodamine 6G by one- and two-photon induced confocal fluorescence microscopy. ChemPhysChem 6:791–804. Eggeling C, Widengren J, Brand L, Schaffer J, Felekyan S, Seidel CAM. 2006. Analysis of photobleaching in single-molecule multicolor excitation and forster resonance energy transfer measurement. J Phys Chem A 110:2979–2995. Ehrenberg M, Rigler R. 1974. Rotational Brownian motion and fluorescence intensity fluctuations. Chem Phys 4:390–401. Enderlein J, Gregor I, Patra D, Dertinger T, Kaupp UB. 2005. Performance of fluorescence correlation spectroscopy for measuring diffusion and concentration. Chemphyschem 6:2324–2336. F€ olling J, Bossi M, Bock H, Medda R, Wurm CA, Hein B, Jakobs S, Eggeling C, Hell SW. 2008. Fluorescence nanoscopy by groundstate depletion and single-molecule return. Nat Method 5:943–945. Gregor I, Patra D, Enderlein J. 2005. Optical saturation in fluorescence correlation spectroscopy under continuous-wave and pulsed excitation. ChemPhysChem 6:164–170.

536

€ A. SCHONLE ET AL.

Haustein E, Schwille P. 2003. Ultrasensitive investigations of biological systems by fluorescence correlation spectroscopy. Methods 29: 153–166. Hell SW. 2007. Far-field optical nanoscopy. Science 316:1153–1158. Hell SW, Kroug M. 1995. Ground-state depletion fluorescence microscopy, a concept for breaking the diffraction resolution limit. Appl Phys B 60:495–497. Kasha M. 1960. Paths of molecular excitation. Radiat Res 2(Suppl): 243–275. Kask P, Palo K, Ullmann D, Gall K. 1999. Fluorescence-intensity distribution analysis and its application in biomolecular detection technology. Proc Natl Acad Sci USA 96:13756–13761. Khoroshilova EV, Nikogosyan DN. 1990. Photochemistry of uridine on high-intensity laser UV irradiation. J Photochem Photobiol B: Biol 5:413–427. Magde D, Webb WW, Elson E. 1972. Thermodynamic fluctuations in a reacting system—Measurement by fluorescence correlation spectroscopy. Phys Rev Lett 29:705–708. Moerner WE. 2007. New directions in single-molecule imaging and analysis. Proc Natl Acad Sci USA 104:12596–12602. Moerner WE, Orrit M. 1999. Illuminating single molecules in condensed matter. Science 283:1670–1676. Moneron G, Medda R, Hein B, Giske A, Westphal V, Hell SW. 2010. Fast STED microscopy with continuous wave fiber lasers. Opt Express 18:1302–1309. Pawley JB. 2006. Handbook of biological confocal microscopy. New York: Springer. 700 p. Rasnik I, McKinney SA, Ha T. 2006. Nonblinking and longlasting single-molecule fluorescence imaging. Nat Method 3:891–893. Redmond RW, Kochevar IE, Krieg M, Smith G, McGimpsey WG. 1997. Excited state relaxation in cyanine dyes: A remarkably efficient reverse intersystem crossing from upper triplet levels. J Phys Chem Part A 101:2773–2777. Reindl S, Penzkofer A. 1996. Higher excited-state triplet-singlet intersystem crossing of some organic dyes. Chem Phys 211:431–439. Reuther A, Laubereau A, Nikogosyan DN. 1996. Primary photochemical processes in water. J Phys Chem 100:16794–16800. Richards B, Wolf E. 1959. Electromagnetic diffraction in optical systems. 2. Structure of the image field in an aplanatic system. Proc R Soc Lond A—Math Phys Sci 253:358–379. Ringemann C, Schonle A, Giske A, von Middendorff C, Hell SW, Eggeling C. 2008. Enhancing fluorescence brightness: Effect of reverse intersystem crossing studied by fluorescence fluctuation spectroscopy. Chemphyschem 9:612–624. Sch€ atzel K, Drewel M, Stimac S. 1988. Photon correlation measurements at large lag times: Improving statistical accuracy. J Modern Opt 35:711–718.

Steinhauer C, Forthmann C, Vogelsang J, Tinnefeld P. 2008. Superresolution microscopy on the basis of engineered dark states. J Am Chem Soc 130:16840–16841. Tsien RY. 2003. Imagining imaging’s future. Nat Cell Biol SS16-SS21. Tsien RY, Ernst L, Waggoner A. 2006. Fluorophores for confocal microscopy: Photophysics and photochemistry. In: Pawley JB, editor. Handbook of biological confocal microscopy, 3rd ed. New York: Springer. pp 338–352. van de Linde S, Kasper R, Heilemann M, Sauer M. 2008. Photoswitching microscopy with standard fluorophores. Appl Phys B 93: 725–731. Vogelsang J, Kasper R, Steinhauer C, Person B, Heilemann M, Sauer M, Tinnefeld P. 2008. A reducing and oxidizing system minimizes photobleaching and blinking of fluorescent dyes. Angew Chem (Int Ed) 47:5465–5469. Vukojevic V, Heidkamp M, Minga Y, Johansson B, Tereniusa L, Rigler R. 2008. Quantitative single-molecule imaging by confocal laser scanning microscopy. Proc Natl Acad Sci USA 105:18176– 18181. Webb WW, Wells KS, Sandison DR, Strickler J. 1990. Criteria for quantitative dynamical confocal fluorescence imaging. In: Herman B, Jacobson K, editors. Optical microscopy for biology. New York: Wiley. pp. 73–108. Weiss S. 1999. Fluorescence spectroscopy of single biomolecules. Science 283:1676–1683. Widengren J, Rigler R. 1990. Ultrasensitive detection of single molecules using fluorescence correlation spectroscopy. In: Klinge B, Owman C, editors. BioScience. Lund: Lund University Press. pp. 180–183. Widengren J, Schwille P. 2000. Characterization of photoinduced isomerization and back-isomerization of the cyanine dye cy5 by fluorescence correlation spectroscopy. J Phys Chem Part A 104:6416– 6428. Widengren J, Seidel CAM. 2000. Manipulation and characterization of photo-induced transient states of Merocyanine 540 by fluorescence correlation spectroscopy. Phys Chem Chem Phys 2:3435– 3441. Widengren J, Rigler R, Mets U. 1994. Triplet-state monitoring by fluorescence correlation spectroscopy. J Fluoresc 4:255–258. Widengren J, Mets U, Rigler R. 1995. Fluorescence correlation spectroscopy of triplet-states in solution—A theoretical and experimental-study. J Phys Chem 99:13368–13379. Widengren J, Chmyrov A, Eggeling C, Lofdahl PA, Seidel CAM. 2007. Strategies to improve photostabilities in ultrasensitive fluorescence spectroscopy. J Phys Chem Part A 111:429–440. Xie XS, Trautmann JK. 1998. Optical studies of single molecules at room temperature. Annu Rev Phys Chem 49:441–480.

Microscopy Research and Technique