Photobleaching of Fluorescent Dyes under Conditions Used for Single

Anal. Chem. 1998, 70, 2651-2659

Photobleaching of Fluorescent Dyes under Conditions Used for Single-Molecule Detection: Evidence of Two-Step Photolysis C. Eggeling,† J. Widengren,‡ R. Rigler,‡ and C. A. M. Seidel*,†

Max-Planck-Institut fu¨ r Biophysikalische Chemie, Am Fassberg 11, D-37077 Go¨ ttingen, Germany, and Department of Medical Biophysics, Karolinska Institut, S-10401 Stockholm, Sweden

The photostability of fluorescent dyes is of crucial importance for the statistical accuracy of single-molecule detection (SMD) and for the image quality of scanning confocal microscopy. Concurrent results for the photostability were obtained by two different experimental techniques. First, the photostabilities of several coumarin and rhodamine derivatives in aqueous solution were obtained by monitoring the steady-state fluorescence decay in a quartz cell. Furthermore, an epi-illuminated microscope, continuous wave (CW) excitation at 514.5 nm, and fluorescence correlation spectroscopy (FCS) with a newly developed theory were used to study the photobleaching characteristics of rhodamines under conditions used for SMD. Depending on the rhodamine structure, the probability of photobleaching, pb, is in the order of 10-6-10-7 for irradiances below 103 W/cm2. However, a considerable increase of pb for irradiances above this level was observed which can only be described by photobleaching reactions from higher excited states (two-step photolysis). In view of these observations, the probability of photobleaching, pb, as well as a closed expression of its dependence on the CW excitation irradiance considering a five-level molecular electronic state model with the possibility of photobleaching from higher excited electronic states, is derived. From this model, optimal conditions for SMD with respect to the number of emitted fluorescence photons and to the signal-to-background ratio are discussed, taking into account both saturation and photobleaching. The additional photobleaching due to two-step photolysis limits the applicable irradiance. Laser-induced fluorescence detection is used for various ultrasensitive analytical techniques in chemistry, biology, and medicine by probing reagents that are either autofluorescent or tagged with a fluorescent dye molecule.1,2 By applying different * Corresponding author. E-mail: [email protected]. † Max-Planck-Institut fu ¨ r Biophysikalische Chemie. ‡ Karolinska Institut. (1) (a) Eigen, M.; Rigler, R. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 5740-47. (b) Rigler, R. J. Biotech. 1995, 41, 177-86. (2) (a) Keller, R. A.; Ambrose, W. P.; Goodwin, P. M.; Jett, J. H.; Martin, J. C.; Wu, M. Appl. Spectrosc. 1996, 50, 12-32. (b) Jett, J. H.; Keller, R. A.; Martin, J. C.; Marrone, B. L.; Moyzis, R. K.; Ratliff, R. L.; Seitzinger, N. K.; Shera, E. B.; Stewart, C. C. J. J. Biomol. Struct. Dyn. 1989, 7, 301-09. S0003-2700(98)00027-4 CCC: $15.00 Published on Web 05/29/1998

© 1998 American Chemical Society

microscopic techniques, various groups have directly visualized a variety of single fluorescent dye molecules dissolved in liquids by using coherent one- and two-photon excitation, e.g., rhodamines3-7 and coumarins.8,9 For a satisfactory signal-to-background ratio, it is crucial to choose a dye with good fluorescence properties. The suitability of a dye is determined by its absorption coefficient as well as its fluorescence, triplet, and photobleaching quantum yields.8-11 Among these properties, the photostability is of major importance, since it leads to the irreversible loss of fluorescence, which limits the statistical accuracy of the detection. The probability of a dye to survive a certain number of excitation cycles before being photobleached is exponentially distributed. This implies that the possibility of an instantaneous photobleaching reaction is highest and that the number of detected photons due to a single-molecule transit through the detection volume can vary significantly. If one strives for an ultimate sensitivity as needed for singlemolecule detection (SMD), an efficient excitation irradiance must be applied. Previous work10 on the optimization of high-sensitivity fluorescence detection did not take into account the fact that molecules in the first electronic excited singlet and triplet states, S1 and T1, may be subject to so-called two-step excitation, where the molecules are excited to higher electronic states, Sn and Tn, by absorption of a second photon. Because these states couple quite efficiently with ionic states in polar solvents like water, twostep and multistep absorption processes open additional channels (3) (a) Shera, E. B.; Seitzinger, N. K.; Davis, L. M.; Keller, R. A.; Soper, S. A. Chem. Phys. Lett. 1990, 174, 553-57. (b) Soper, S. A.; Davis, L. M.; Shera, E. B. J. J. Opt. Soc. Am. B 1992, 9, 1761-69. (4) (a) Rigler, R.; Mets, U ¨ . SPIE Proc. 1992, 1921, 239-48. (b) Mets, U ¨ .; Rigler, R. J. Fluoresc. 1994, 4, 259-64. (5) Mertz, J.; Xu, C.; Webb, W. W. Opt. Lett. 1995, 20, 2532-34. (6) Zander, C.; Sauer, M.; Drexhage, K. H.; Ko, D.-S.; Schulz, A.; Wolfrum, J.; Brand, L.; Eggeling, C.; Seidel, C. A. M. Appl. Phys. B 1996, 63, 517-23. (7) (a) Sauer, M.; Drexhage, K. H.; Zander, C.; Wolfrum, J. Chem. Phys. Lett. 1996, 254, 223-28. (b) Mu ¨ ller, R.; Zander, C.; Sauer, M.; Deimel, M.; Ko, D.-S.; Siebert, S.; Arden-Jacob, J.; Deltau, G.; Marx, N. J.; Drexhage, K. H.; Wolfrum, J. Chem. Phys. Lett. 1996, 262, 716-22. (8) Brand, L.; Eggeling, C.; Zander, C.; Drexhage, K. H.; Seidel, C. A. M. J. Phys. Chem. A 1997, 101, 4313-21. (9) Eggeling, C.; Brand, L.; Seidel, C. A. M. Bioimaging 1997, 5, 105-15. (10) (a) Hirschfeld, T. Appl. Opt. 1976, 15, 12, 3135-39. (b) Mathis, R. A.; Peck, K.; Stryer, L. Anal. Chem. 1990, 62, 1786-91. (c) Enderlein, J. Appl. Opt. 1995, 34, 514-26. (11) Tsien, R. Y.; Waggoner, A. In The Handbook of for Biological Confocal Microscopy; Pawley, J. B., Ed.; Plenum Press: New York, 1995; pp 267-79.

Analytical Chemistry, Vol. 70, No. 13, July 1, 1998 2651

for photobleaching.12,13 This two-step photolysis is readily obtained by the use of pulsed lasers, as shown previously in the case of coumarins9,14 and Rhodamine 6G.15 The photobleaching following pulsed excitation depends on the peak irradiance as well as on the repetition rate.9 In confocal scanning microscopy, irradiances as high as 250 kW/cm2 are applied to minimize the data acquisition time per pixel. However, it is still relatively unknown if and to what extent the bleaching efficiency under these conditions may drastically influence the image quality.11 The photostability of a dye can be characterized by its quantum yield of photobleaching, φb. In the case of Rhodamine 6G in water, φb has been determined by various groups.16 However, different experimental approaches, dye concentrations, excitation irradiances, and definitions of φb have been applied, resulting in a wide range of values between 0.2 × 10-5 and 2.5 × 10-5. Recently, fluorescence correlation spectroscopy (FCS) was introduced as a means to investigate the photostabilities of dyes. A strong dependence on the excitation irradiance was found that could not be explained by an electronic state model using only ground singlet and first excited singlet and triplet states.16d Hence, questions on the optimization of SMD with regard to photobleaching still remain open. In this report, we consider in detail the excitation to higher excited electronic states, Sn and Tn, and give precise definitions of several photobleaching parameters with a closed expression of their dependence on the excitation irradiance. We experimentally determine φb for several coumarin and rhodamine dyes in a wide concentration range using two approaches: (1) a cellbleaching setup applying irradiances below 103 W/cm2 and (2) an epi-illuminated microscope together with FCS to study the irradiance dependence of φb for rhodamines. The approach presented describes the limits for the optimization of SMD. EXPERIMENTAL SECTION The fluorescent dyes (Coumarin 120, Coumarin 307, and Coumarin 102, Lambda Physik, Go¨ttingen, FRG; Carbostyril 124 and Rhodamine 123 chloride, Sigma, Deisenhofen, FRG; Coumarin 39, a kind gift from Prof. Drexhage, Gesamthochschule Siegen, FRG; Rhodamine 6G chloride, Radiant Dyes, Wermelskirchen, FRG; and Tetramethylrhodamine ethyl ester perchlorate, Molecular Probes, Eugene, OR) were used without further purification. The dye solutions for the experiments were prepared by dilution in double-distilled water from 10-3 M stock solutions. The (12) (a) Nikogosyan, D. N. Laser Chem. 1987, 7, 29-34. (b) Khoroshilova, E. V.; Nikogosyan, D. N. J. Photochem. Photobiol. B: Biol. 1990, 5, 413-27. (c) Hart, E. J.; Anbar, M. The Hydrated Electron; Wiley Interscience: New York, 1970. (d) Anbar, M.; Hart, E. J. J. Am. Chem. Soc. 1964, 86, 563337. (13) Reuther, A.; Nikogosyan, D. N.; Laubereau, A. J. Phys. Chem. 1996, 100, 5570-77. (14) (a) Seidel, C. A. M. Ph.D. thesis, Ruprecht-Karls-Universita¨t, Heidelberg, 1992. (b) Eggeling, C. Diploma thesis, Georg-August-Universita¨t, Go¨ttingen, 1996. (15) Aristov, A. V. Opt. Spectrosc. 1994, 77, 6, 856-57. (16) (a) Rosenthal, I. Opt. Commun. 1978, 24, 164-66. (b) Beer, D.; Weber, J. Opt. Commun. 1972, 5, 4, 307-09. (c) Soper, S. A.; Nutter, H. L.; Keller, R. A.; Davis, L. M.; Shera, E. B. Photochem. Photobiol. 1993, 57, 972-77. (d) Widengren, J.; Rigler, R. Bioimaging 1996, 4, 149-57. (e) Schmidt, Th.; Schu ¨ tz, G. J.; Baumgartner, W.; Gruber, H. J.; Schindler, H. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 2926-29. (f) Huston, A. L.; Reimann, C. T. Chem. Phys. 1991, 149, 401-07. (g) Mathis, H., Institute of Molecular Biology (IMB), Jena, Germany. Personal communication, 1997.

2652 Analytical Chemistry, Vol. 70, No. 13, July 1, 1998

absorption cross sections, σ01, of the dyes in water and ethanol were determined by measuring the optical density of the exactly weighed in dye solutions at a Cary-5E UV-visible-near-IR spectrometer. Their values in ethanol are in good agreement with those reported by Brackmann.17 All experiments were done in air-saturated solutions at 25 °C. In the setup of the cell-bleaching experiment,9 a mercury arc lamp (Osram, HBO 100W/2) with appropriate interference filters (365.7, 334, or 397 nm, Schott, Mainz, FRG) or a continuous wave (CW) argon ion laser (Innova Sabre, Coherent, Palo Alto, CA) at 514.5 nm serves as excitation light source. The excitation light is focused into the quartz cell (1 × 1 cm2) containing the constantly stirred dye solution. Using an appropriate long-pass filter (Schott), the fluorescence light is detected perpendicular to the excitation light by a photodiode (S1226-8BQ, Hamamatsu, Hamamatsu City, Japan) or a bialkali photomultiplier (R5600P-03, Hamamatsu). A part of the excitation light is monitored by a second photodiode to correct for possible fluctuations. The two time-dependent amplified signals are read into a computer by an analog-to-digital converter PC board (WIN 30D, Meilhaus Electronic, Puchheim, FRG). The setup of the confocal epi-illuminated fluorescence microscope16d uses the excitation light of a CW argon ion laser (Spectra Physics model 165, Mountain View, CA) at 514.5 nm, which is focused by a lens (focal length ) 600 mm) in front of the microscope and coupled into the objective (Zeiss Plan-Neofluar 63× NA 1.2, water immersion) via a dichroic mirror (Leitz TK580). The fluorescence light of the sample placed beneath the objective is collected and imaged onto a pinhole (diameter 250 µm) by the same objective. Afterward, the light is divided by a beam splitter and detected (interference filter, 565DF50 or 585DF50, Omega Optics) by two avalanche photodiodes (model SPCM-100, EG&G, Vaudreuil, Quebec, Canada), whose pulses are computed by a PC-adapted correlator (model 5000/E, ALV, Langen, FRG). The excitation power at the sample was measured by using a power meter (fieldmaster, Coherent). THEORY Quantum Efficiency of Photobleaching. The photobleaching of a dye solution can be characterized by the quantum yield of photobleaching, φb, or the photobleaching probability, pb. Usually, photophysical and photochemical reactions are characterized by a quantum yield. The quantum yield of a photobleaching reaction is equal to the number of molecules that have been photobleached, divided by the total number of photons absorbed during the same time interval (eq 1).12a It is important to note

φb )

number of photobleached molecules total number of absorbed photons

(1)

that the total number of absorbed photons also includes those photons absorbed in a second step leading to higher excited electronic states, which open up new bleaching channels.12,13 However, since the fluorescence emission is usually related to the first excited singlet state, S1, it is crucial for the accuracy of experiments such as single-molecule fluorescence detection to (17) Brackmann, U. Lamdachrome Laser Dyes, 2nd ed.; Lamda Physics GmbH: Go ¨ttingen, 1994.

(cm2), at a wavelength λ (eq 4), where γ ) λ/(hcl) is the inverted photon energy (h is the Plank constant and cl the velocity of light).

k(T)if(λ) ) Iσ(T)if(λ)γ

(4)

kf, kIC, and kISC are the depopulation rate constants of S1 by fluorescence emission, internal conversion, and intersystem crossing to T1, respectively. The lifetime, τ0, of the S1 state (fluorescence lifetime) is then

τ0 ) 1/k0 ) 1/(kf + kIC + kISC)

Figure 1. Electronic energy diagram of a dye molecule with five electronic levels regarding photobleaching from every electronic level (for details, see text). Inset: Basic model of the photobleaching reaction from a higher electronic excited state, Xn (X ) S or T), involving the formation of an ion pair, (M+e-), and following excitation from the first electronic excited state, X1 (for details, see Appendix A).

know the probability of photobleaching, pb, at a certain applied excitation irradiance. This is equal to the number of photobleached molecules divided by the mean number of molecules in the S1 state for a given time interval (eq 2). Unfortunately, the

pb )

number of photobleached molecules number of molecules in S1

(2)

total number of absorbed photons as well as the mean number of molecules in the S1 state cannot be measured precisely under the experimental conditions of SMD, which makes it impossible to determine φb and pb directly. However, it is possible to measure the number of irreversibly photobleached molecules as a decrease in the dye concentration, c(t), with time, t. The photobleaching reaction can be regarded as a quasi-unimolecular reaction. This assumption results in an exponential decrease of the dye concentration (eq 3).9,10 c0 is the initial concentration at time t ) 0 and kz is the effective pseudo-first-order bleaching rate constant.

c(t) ) c0 exp(-kzt)

(3)

(5)

The depopulations of T1 to S0, Sn to S1, and Tn to T1 are described by the rate constants kT, kSn1, and kTn1, respectively. The rate constant k′ISC for intersystem crossing from Sn to Tn is neglected due to the short lifetimes of these states. Photobleaching in the “Low” Excitation Irradiance Range (Three-Level System). As long as the fluorescence flow depends linearly on the excitation irradiance, like in the cell-bleaching experiments, the probability of a molecule to be in a first excited electronic state, S1 or T1, is very low. Hence, the absorption of a second photon by S1 and T1 (k(T)1n) can be neglected, and the electronic five-level system described above reduces to a threelevel system with the states S0, S1, and T1. The time, t, behavior of the three-level scheme following CW excitation is described by the population probabilities, S0(t), S1(t), and T1(t), of a dye molecule to be in S0, S1, or T1 (see eqs 10-14 of ref 20a). Because the rate constants of photobleaching are usually much smaller than the other relevant rate constants, it is appropriate to use the 3 3 3 steady-state population probabilities, S0eq , S1eq , and T1eq (eq 6), for the analysis of photobleaching. Consequently, the whole three3 S0eq )

k0kT k01(kISC + kT) + k0kT

3 ; S1eq )

k01 3 S ; k0 0eq 3 ) T1eq

kISC 3 S (6) kT 1eq

level system can be treated as a one-level system with respect to photobleaching from any state, allowing no selective depopulation of a special electronic state. If bleaching occurs only from S1 and T1, the effective bleaching rate constant, kz ) k3z , is determined by the microscopic rate constants, kbS and kbT, and by the triplet parameters, kISC and kT. 3 3 3 3 k3z ) kbSS1eq + kbTT1eq ) (kbS + kbTkISC/kT)S1eq ) kbS1eq

In the following section, we will derive expressions to describe the dependence of the experimentally accessible parameter kz as well as of the photobleaching parameters φb and pb on the CW irradiance. Molecular Electronic States. Figure 1 shows the electronic energy diagram of a dye molecule with five electronic levels: ground singlet state, S0, first excited singlet state, S1, lowest excited triplet state, T1, and higher excited singlet and triplet states, Sn and Tn. Photobleaching reactions are assumed to be possible from all excited states with the microscopic rate constants kbS, kbT, kbSn, and kbTn respectively. The rate constants k(T)if for excitation from a state i to a state f are proportional to the irradiance, I (W/cm2), and to the absorption cross section, σif(λ)

(7) This dependence can be expressed by the composite microscopic rate constant, kb, of photobleaching from S1 and T1 (eq 7), with kb ) (kbS + kbTkISC/kT). Using the steady-state populations of a threelevel system (eq 6), the dependence of k3z on the excitation irradiance, I, is given by

k3z (I) )

kbI 3 I/S1eq,max

+ k0/(σ01γ)

(8)

The absorption cross section, σ01, and the rate constant, k0, were Analytical Chemistry, Vol. 70, No. 13, July 1, 1998

2653

3 previously defined in eqs 4 and 5, respectively. S1eq,max ) kT/(kT + kISC) is the saturation steady-state population of S1 of a threelevel system. Equation 6 reduces to this expression for high irradiances (k01 ) I(σ01γ) . k0). Considering only a three-level system, the effective photobleaching rate constant, k3z , describes a straight line with the slope kbσ01γ/k0 for very low values of I (I/ 3 S1eq,max , k0/(σ01γ)), whereas for higher values it levels off due to saturation of the S0-S1 transition. Thus, from eqs 1 and 2, one obtains for a three-level system

φ3b(I) )

k3z 3 k01S0eq

)

kb k3z ) ) p3b(I) ) constant k0 k S 3 0 1eq

(9)

where φ3b(I) is independent of I and equivalent to p3b(I). Photobleaching in the “High” Excitation Irradiance Range (Five-Level System). At excitation irradiances necessary for effective SMD, the population of Sn and Tn due to two-step excitation becomes important. Therefore, a five-level system (Figure 1) has to be considered. Defining Sn(t) and Tn(t) as the population probabilities of the dye molecule to be in Sn or Tn at time t following CW excitation, the steady-state population probabilities of this system can be calculated analogously to the threelevel scheme with S0(t) + S1(t) + T1(t) + Sn(t) + Tn(t) ) 1 (eq 10a) (see Figure 1 for explanation of rate constants), with X ) kTn1[kT(kSn1(k0 + k01) + k01k1n)] + (kT1n + kTn1)(kISCkSn1k01). 5 S0eq )

kTn1kSn1kTk0 X Sneq )

5 S1eq )

k1n 5 S kSn1 1eq

k01 5 S k0 0eq Tneq )

5 T1eq )

kISC 5 S kT 1eq

kT1n 5 S kTn1 1eq

(10a)

5 The irradiance dependence of S1eq of the five-level system is similar to that of a three-level system: (1) linear dependence for low irradiances (k01 , k0); (2) saturation, then reaching a 3 maximum value of S1eq,max (eq 8); and (3) in contrast to the three-level model, a decrease for very high irradiances (k1n,kT1n 5 . kSn1,kTn1) according to S1eq,high (I) or the two-step saturation factor, Σ5, of eq 10b. Because Sn and Tn open up new channels

5 S1eq,high (I)

1 ) ) Σ5I 1 (10b) [(1/kSn1)σ1nγ + (kISC/kT)(1/kTn1)σT1nγ]I

for photobleaching (two-step photolysis, see Appendix A in Supporting Information), the effective bleaching rate constant, kz ) k5z , is a sum of the composite microscopic bleaching rate constants, kb, of the first excited electronic states, S1 and T1 (eq 7), and kbnI of the higher excited electronic states, Sn and Tn (eq 11), with kbn ) (kbSn/kSn1)σ1nγ + (kISC/kT)(kbTn/kTn1)σT1nγ.

for a five-level system is obtained (eq 12).

k5z (I) )

kbnI2 + kbI 3 Σ5I2 + I/S1eq,max + k0/(σ01γ)

(12)

k5z (I) strongly depends on I and reduces to k3z (I) for I , kb/kbn. From the definition of eq 2, the probability of photobleaching, p5b(I), for a five-level system is given by

p5b(I) )

k5z 5 k0S1eq

)

kbnI + kb kbn kbn ) I + p3b ) I + φ3b k0 k0 k0

(13)

The terms “low” and “high” irradiance are used throughout this report to illustrate the irradiance ranges where the simplification of the three-level system is sufficient and where the use of the five-level system is necessary to explain the photobleaching properties of a dye. Let us define the two-step threshold irradiance, I2step, to distinguish between these two irradiance ranges. For irradiances above kbnI2step ) kb, a marked increase of the effective bleaching rate constant, k5z (I), and of the photobleaching probability, p5b(I), can be deduced from eq 11 or 13 due to additional two-step excitation (high irradiance range), whereas for irradiances below kbnI2step ) kb, both k5z (I) and p5b(I) reduce to the classical expressions, k3z and p3b, of the threelevel system (low irradiance range). Consequently, in the case of Rhodamine 6G, a two-step threshold irradiance, I2step ) 5.6 × 104 W/cm2, can be calculated, if the parameters of Table 2 are employed. However, one has to keep in mind that I2step is a characteristic dye-specific property. Its value severely influences the suitability of a dye with regard to high irradiance measurements. Cell-Bleaching. The cell-bleaching experiment measures the time-dependent decrease of the fluorescence flow, F(t), of an illuminated and stirred dye solution due to irreversible photobleaching with the effective rate constant kz at excitation irradiances below 103 W/cm2, whereby F0 is the fluorescence flow at time t ) 0 (eq 14).

F(t) ) F0 exp(-kzt) ) gdΦfS1eqc0Vill(1/τ0) exp(-kzt) (14)

F(t) is proportional to the concentration of dye molecules in S1 within the illumination volume (S1eqc(t)) (eqs 3 and 6), the fluorescence quantum yield, Φf ) kf/k0, of the dye, the fluorescence detection efficiency, gd, of the setup, the illumination volume, Vill, and the inverse of the fluorescence lifetime, 1/τ0. The final dependence of φ3b on the experimental parameters of the cell-bleaching method (eq 15) assumes S0eq ) 1 due to the

φ3b )

Vsol kz σ01γbc P

(15)

5 5 k5z ) kbSnSneq + kbTnTneq + kbSS1eq + kbTT1eq ) 5 (11) (kb + kbnI)S1eq

Using eq 10, the dependence of k5z on the excitation irradiance, I, 2654 Analytical Chemistry, Vol. 70, No. 13, July 1, 1998

low excitation irradiances and takes into account that only a fraction, Rill, of the dye solution with the total volume Vsol is illuminated in the cell. This fraction is given by Rill ) Vill/Vsol ) Aillbc/Vsol (Aill is the focal area of the excitation light beam and bc

the optical path length in the cell). P (W) is the excitation power (P ) IAill) and can be measured by using a power meter. Photochemical Parameters Observed by FCS. Higher excitation irradiances (I > 104 W/cm2) can be achieved using laser excitation in a confocal epi-illuminated fluorescence microscope. This arrangement allows for the observation of even single fluorescent molecules in a small, open-volume element of a few femtoliters size. Concentration fluctuations of the fluorescent molecules in this volume element due to diffusion or chemical reactions cause fluorescence fluctuations, δF(t), about an average value, 〈F(t)〉 (F(t) ) 〈F(t)〉 + δF(t)). In FCS,18 these fluctuations are analyzed by an autocorrelation function, G(tc), with the correlation time, tc (eq 16).

G(tc) )

〈F(t)F(t + tc)〉 〈F(t)〉2

)1+

〈δF(t)δF(t + tc)〉 〈F(t)〉2

(16)

be described by G(tc) using the effective bleaching rate constant, kz.14b,16d Yet, it is important to note that kz depends on the irradiance (eq 12) and, thus, on space. A straightforward analytical solution does not exist for such an autocorrelation function. Hence, we made the simplifying assumption of a rectangular excitation profile with radius ω0 and height z0(π/8)1/2.20b,21 This assumption defines an average effective photobleaching rate constant, kz,av(I0/2), over the whole excitation volume with the focal irradiance I0 ) I(z ) 0) (eq 18). The autocorrelation function,

kz ≈

{

kz,av(I0/2); x2 + y2 e ω20; |z| e z0xπ/8 0; elsewhere

(

)(

)

1 1 1 GD(tc) ) N 1 + tc/τD 1 + (ω /z )2(t /τ ) 0 0 c D

1/2

(17)

The spatial distribution of the detected fluorescence is assumed to be three-dimensional Gaussian (W(x,y,z) ) exp(-2(x2 + y2)/ ω02) exp(-2(z2)/z02)).19 The characteristic time of diffusion, τD, of the fluorescent molecules through the detection volume is given by τD ) ω02/4D. D is the translational diffusion coefficient of the observed dye molecules, and ω0 is the distance from the beam center in the radial direction at which W(x,y,z) has dropped by a factor of e2. For a chemical reaction, the fluorescent molecules detected in the volume element participate in the thermodynamic equilibrium, generating additional signal fluctuations with characteristic time constants in the autocorrelation function.18 However, for the special case of a photochemical reaction, this theory has to be modified since the reaction is restricted to the excitation volume. Two different photochemical reactions have to be taken into account: (1) triplet formation in a reversible photochemical equilibrium20 and (2) irreversible first-order photobleaching reaction to a nonfluorescent product.14b,16d,18e Because the total sample volume is much larger than the excitation volume, the depletion of fluorophores within the excitation volume will be balanced by a net in-flow from outside due to the concentration gradient formed. Thus, under our experimental conditions, photobleaching can be treated as a chemical pseudoequilibrium reaction and can (18) (a) Magde, D.; Elson, E. L.; Webb, W. W. Phys. Rev. Lett. 1972, 29, 70508. (b) Elson, E. L.; Magde, D. Biopolymers 1974, 13, 1-27. (c) Ehrenberg, M.; Rigler, R. Chem. Phys. 1974, 4, 390-410. (d) Thompson, N. L. In Topics in Fluorescence Spectroscopy; Lakowicz, J. R., Ed.; Plenum Press: New York, 1991; Vol. 1, pp 337-78. (e) Enderlein, J. Phys. Lett. A 1996, 221, 427-33. (19) (a) Rigler, R.; Widengren, J. BioScience; Lund University Press: Lund, 1990; pp 180-83. (b) Rigler, R.; Mets, U ¨ .; Widengren, J.; Kask, P. Eur. Biophys. J. 1993, 22, 169-75. (c) Aragon, S. R.; Pecora, R. J. Phys. Chem. 1976, 64, 1791-803. (20) (a) Widengren, J.; Mets, U ¨ .; Rigler, R. J. Phys. Chem. 1995, 99, 13368-79. (b) Widengren, J.; Rigler, R.; Mets, U ¨ . J. Fluoresc. 1994, 4 (3), 255-58.

(18)

G(tc), is then given by eq 19 (Appendix B in Supporting Information)14b with 1/tT ) (kT + (k01kISC)/(k01 + k0)). T1eq is the

G(tc) ) 1 + If translational diffusion is the only noticeable process that causes fluorescence fluctuations, the time-dependent part, GD(tc), of the normalized correlation function, G(tc) (eq 16), is given by eq 17.

}

GD(tc)

[1 - A(1 - T1eq) + A(1 - T1eq) ×

(1 - T1eq)

exp(-kz,av(I0/2)tc) - T1eq + T1eq exp(-tc/tT)] (19)

average equilibrium fraction of molecules in T1 (eq 6) with an average triplet correlation time, tT.20 By assuming an average effective photobleaching rate constant, kz,av, the actual spacedependent homogeneous distribution of bleaching reactions with kz(I(x,y,z)) on all molecules in the whole excitation volume is changed into an overall bleaching reaction with kz,av(I0/2) of only a fraction, A, of all excited molecules. The theoretically expected fraction, A ) 0.8 (Appendix B in Supporting Information), is in good agreement with values of about 0.75 from the fits of eq 19 to the experimental data shown below. RESULTS AND DISCUSSION Photobleaching in Aqueous Solution Observed by the Cell-Bleaching Method. The cell-bleaching method was used to determine the quantum yield of photobleaching, φ3b, at low excitation irradiances for several frequently used laser dyes in air-saturated, aqueous solutions. Figure 2 shows the timedependent exponential decrease of the fluorescence flow, F(t), of a Rhodamine 6G solution (10-6 M, Vsol ) 1 mL) excited with P ) 2 W at 514.5 nm. The residuals of a fit with one and two exponential decay constants (Figure 2A,B) clearly indicate that only a double-exponential fit is adequate. This is also the case for the bleaching curves of the other dyes investigated. Figure 2C shows that the fluorescence flow of an aqueous dye solution drops even without illumination, reaching a steady-state level. Detailed investigations on all dyes showed that this initial signal drop increases with decreasing dye concentration and correlates with the hydrophobic properties of the dyes. This would suggest that the drop is caused by unspecific adsorption of the dye to the cell surface and not by precipitation due to the limited solubility of the organic dyes in water, which is also supported by other investigators.22 Furthermore, in the presence of detergents like (21) Siegman, A. E. Lasers; University Science Books: Mill Valley, CA, 1986. (22) (a) Do¨rre, K.; Brakmann, S.; Brinkmeier, M.; Han, K.-T.; Riebeseel, K.; Schwille, P.; Stephan, J.; Wetzel, T.; Lapczyna, M.; Stuke, M.; Bader, R.; Hinz, M.; Seliger, H.; Holm, J.; Eigen, M.; Rigler, R. Bioimaging 1997, 5, 139-52. (b) Enderlein, J.; Goodwin, P. M.; van Orden, A.; Ambrose, W. P.; Erdmann, R.; Keller, R. A. Chem. Phys. Lett. 1997, 270, 464-70.

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Figure 2. Time-dependent exponential decrease of the fluorescence signal, F(t), of a stirred Rhodamine 6G solution (1 mL, 10-6 M in water) in a cell excited by a CW argon ion laser with P ) 2 W at 514.5 nm. Insets A and B show the weighted residuals of a single (A) and double (B) exponential fit to the data: single, F(t) ) 0.02 + 0.91 exp(-t/1017 s); double, F(t) ) 0.13 exp(-t/210 s) + 0.85 exp(-t/1080 s). Furthermore, the time-dependent exponential decrease of the fluorescence signal, F(t), of a stirred Rhodamine 6G solution (1 mL, 10-10 M in water) in a cell is shown (C), where the illumination by a CW argon ion laser with P ) 1 W at 514.5 nm is started at a later point in time.

Tween 20, which suppress unspecific adsorption, single-exponential bleaching decays are obtained. Consequently, we treated the decrease of the signal flow by two processes: (1) a reversible adsorption-desorption equilibrium to the cell surface with the rate constants kads and kdes, leading to a dye concentration csolv in solution and cads on the surface, and (2) irreversible photobleaching of the free dye with the rate constant k3z due to illumination: kdes

k3z

cad {\ } csolv 98 bleached dye, cb k ads

Figure 3. Power dependence of the effective bleaching rate constant, kz, of Rhodamine 123 in water excited at 514.5 nm. The dye concentration is varied between 10-6 and 5 × 10-8 M. kz is determined from the exponential decrease of the fluorescence flow of the illuminated stirred dye solution in the cell-bleaching experiment. A linear fit to the data results in slope of 2 × 10-4/(sW) and, thus, in a value of φ3b ) 6.3 × 10-7 (eqs 8 and 9). The inset shows the power dependence of the quantum yield of photobleaching, φ3b, of Rhodamine 6G in water at various concentrations ((O) 10-6, ([) 10-7, (+) 5 × 10-8, and (×) 10-10 M) excited at 514.5 nm. φ3b is calculated from the exponential decrease of the fluorescence flow of the illuminated stirred dye solution in the cell-bleaching experiment using eq 15. Table 1. Photostability Properties of Coumarin and Rhodamine Dyes in Water at Low Irradiances Obtained from the Cell-Bleaching Experiments dye Coumarin 120 Coumarin 307 Coumarin 102 Coumarin 39 Carbostyril 124 Rhodamine 6G TMR Rhodamine 123

φba,b

µa,c

3.4 × 10-4 3 000 1.5 × 10-4 6 500 4.3 × 10-4 2 300 -3 1.2 × 10 800 1.4 × 10-3 700 1.2 × 10-6 833 000 3.3 × 10-7 3 070 000 6.4 × 10-7 1 570 000

τ0 kb (ns)d (s-1)a,e 5.0 4.5 5.5 5.6 5.0 3.9 2.3 4.0

σ01 (λ) (10-17 cm2)

6 700 3.9 (365 nm) 3 400 5.4 (397 nm) 7 800 7.0 (397 nm) 21 000 4.7 (397 nm) 27 000 6.3 (335 nm) 310 22.2 (515 nm) 140 13.3 (515 nm) 160 12.3 (515 nm)

Applying the initial conditions for t ) 0 (csolv(0) ) 1, cad(0) ) 0, and cb(0) ) 0), such a kinetic scheme can be described by two exponentials: csolv(t) ) a1 exp(-λ1t) + a2 exp(-λ2t). The rate constants kdes, kads, and k3z can be extracted from the amplitudes, ax, and rate constants, λx, via the following relations: a1,2 ) (G ( E - 2kdes)/(2G) and λ1,2 ) (E ( G)/2, with the defined constants G ) ((kads + kdes - k3z )2 + 4kdesk3z )1/2 and E ) (kads + kdes + k3z ).14b,23 At various concentrations ranging from 10-5 to 10-10 M, the fluorescence decreases of the dyes were monitored at different excitation powers, P. From the obtained value of k3z , the quantum yield of photobleaching, φ3b, could be calculated by the use of eq 15. While k3z shows the expected linear dependence on P (Figure 3), φ3b is independent of the dye concentration as well as of P (inset of Figure 3), which was predicted in theory (eq 9). This is evidence that a three-level molecular electronic state model and a single-exponential decay is appropriate to describe the bleaching characteristics of the investigated dyes at the given concentrations and excitation irradiances.

Table 1 gives the obtained values of the quantum yield of photobleaching, φ3b, of the different dyes in aqueous solution, the mean number of survived excitation cycles, µ ) 1/p3b ) 1/φ3b, the fluorescence lifetimes, τ0,24 and the rate constant, kb, of photobleaching from the first excited electronic states (eq 7). The photostabilities of the rhodamine derivatives are approximately 2-3 orders of magnitude higher than those of the coumarin derivatives. This can be explained by several arguments: (1) Because the triplet state is proposed to be a major bleaching channel,25 the extremely low triplet quantum yield of rhodamines

(23) Birks, J. B. Photophysics of Aromatic Molecules; J. Wiley & Sons Ltd.: London, 1970; p 304.

(24) The fluorescence lifetimes, τ0, of the dyes were determined from precision measurements at dye concentrations of about 10-7 M.

2656 Analytical Chemistry, Vol. 70, No. 13, July 1, 1998

a The standard deviation of all values is in the order of 20%, obtained by repeated measurements. b The quantum yield of photobleaching, φb ) φ3b, was calculated from the measured fluorescence decreases using eq 15. c The mean number of survived excitation cycles, µ, was calculated from φb: µ ) 1/φb. d The fluorescence lifetimes, τ0, of the dyes were determined from precision measurements at dye concentrations of about 10-7 M. e The composite microscopic rate constant, kb, of photobleaching from S1 and T1 was calculated using eq 9.

(below 1%)20,26 leads to a decreased photobleaching probability. (2) The values of φ3b correlate with the singlet and triplet energies, ES and ET, of the dyes, which are significantly different for coumarins (ES ) 3 eV14a and ET ) 2.5 eV27) and rhodamines (ES ) 2 eV14a and ET ) 1.86 eV28). (3) The coumarin and carbostyryl chromophores are chemically quite reactive.29 Even though the mean number of survived absorption cycles of Coumarin 120 is only 3000, the photostability was found to be sufficiently high to allow SMD by coherent two-photon excitation at 700 nm.8 However, due to their lower photostability, the possibility of single coumarin molecules to emit a certain minimal number of photons necessary for detection at a given threshold is much smaller than that for rhodamine molecules. Therefore, current projects for single-molecule DNA sequencing based on fluorescence detection are using rhodamine dyes as labels.2a,22a The most photostable rhodamine dyes are Rhodamine 123 and Tetramethylrhodamine. Photobleaching in Aqueous Solution Observed by FCS. Using FCS together with a confocal epi-illuminated microscope, we investigated the photobleaching behavior of Rhodamine 6G (Rh6G) (5 × 10-10 M in water) and Tetramethylrhodamine (TMR) (10-9 M in water) at excitation irradiances (I > 104 W/cm2) necessary for SMD. The radius of the excitation volume was deliberately expanded compared to that of SMD experiments4,6,8 to increase the probability of observing photobleaching of the dye molecules due to longer transit times through the excitation volume. Figure 4 shows the autocorrelation curves, G(tc), of the fluorescence fluctuations of the TMR solution for three different excitation irradiances, I0/2, that differ by 1 order of magnitude. For the lowest irradiance (b), photobleaching is negligible, and G(tc) shows only one decay, revealing the characteristic diffusion time through the detection volume. A higher irradiance has two effects on G(tc) (full and dashed line): (1) Due to a more efficient excitation, the triplet state is more populated, resulting in an additional exponential decay in the microsecond time scale.20 (2) Photobleaching becomes evident by an apparently reduced diffusion time.14b,16d Thus, the obtained autocorrelation curves were fitted to eq 17 for excitation irradiances I0/2 < 105 W/cm2 to determine the parameters of the detection volume assuming a diffusion coefficient of D ) 3 × 10-6 cm2/s 20 (τD ) 2.2 ms, ω0 ) 1.63 µm, z0/ω0 ) 2.4) and to eq 19 for excitation irradiances I0/2 > 105 W/cm2 with fixed values of ω0 and z0/ω0 to analyze the photophysical and photochemical parameters. The size of ω0 was also used to obtain the focal excitation irradiance, I0 ) P/(0.5πω02), from the measured excitation power, P. Equation 19 could describe all measured autocorrelation curves at higher irradiances directly, providing values of the average equilibrium fraction, T1eq, and the effective bleaching rate constant, kz,av(I0/2). (25) (a) Song, L.; Varma, C. A. G. O.; Verhoeven, J. W.; Tanke, H. J. Biophys. J. 1996, 70, 2959-68. (b) Korobov, V. E.; Chibisov, A. K. J. Photochem. 1978, 9, 411-24. (c) von Trebra, R.; Koch, T. H. Chem. Phys. Lett. 1982, 93, 4, 315-17. (26) Thiel, E. Habilitation thesis, Universita¨t-GH Siegen, 1995. (27) (a) Priyardasini, K. I.; Naik, D. B.; Moorthy, P. N. Chem. Phys. Lett. 1988, 148, 572-76. (b) Priyardasini, K. I.; Naik, D. B.; Moorthy, P. N J. Photochem. Photobiol. A: Chem. 1990, 54, 251-61. (28) Murov, S. L.; Carmichael, I.; Hug, G. L. Handbook of Photochemistry; Marcel Dekker Inc.: New York, 1993. (29) Kunjappu, J. T.; Rao, K. N. J. Photochem. 1987, 39, 135-43.

Figure 4. Fluorescence autocorrelation curves, G(tc), of TMR (10-9 M in water) for three different excitation irradiances, I0/2, at a wavelength of 514.5 nm. For illustration, the different curves are normalized on each other. Fitting of the FCS curves to eq 19 results in values of the average equilibrium fraction, T1eq, of molecules in T1 and of the average triplet correlation time, tT, which are shown as a function of the applied laser irradiance, I0/2 (inset). The inset also shows a fit of the theoretical expression of T1eq (eq 6) and tT (eq 19) to these data with the fixed parameters σ01 ) 1.33 × 10-16 cm2 and k0 ) 4.35 × 108 s-1. The fit results in values of kISC and kT listed in Table 2.

Triplet Parameters. The inset of Figure 4 shows the obtained values of T1eq (0) and of tT (9) as a function of the applied laser irradiance, I0/2, for TMR. A fit of the theoretical expressions of T1eq (eq 6) and tT (eq 19) to these data, where the values of σ01 and k0 (Table 1) were fixed, resulted in values of kISC and kT listed in Table 2. In the case of Rh6G, these values are in good agreement with the literature.20,25b,26 Because a uniform triplet population is assumed over the whole detection volume and the influence of fluorescence saturation and photobleaching on the triplet state is neglected, the value of kISC differs slightly from that determined by FCS before, where the nonuniform excitation irradiance distribution has been taken into consideration.20a Photobleaching Parameters. Figure 5 shows the obtained values of kz,av(I0/2) for Rh6G (A) and TMR (B) (b) as a function of the applied excitation irradiance, I0/2. The dashed and full curves describe two cases. (1) Dashed curve: If the simple threelevel system is used, kz,av(I0/2) will saturate with increasing I0 due to saturation of the optical transitions (eq 8) in contrast to the experimental results. (2) Full curve: Using the five-level system, a significant increase of kz,av(I0/2) due to additional two-step photolysis is predicted (eq 12), which is concurrent with the obtained results. For the subsequent fit of eq 12 to the data of kz,av(I0/2), the parameters τ0 ) 1/k0 and σ01 (Table 1), kISC ) 1.1 × 106 and kT ) 4.9 × 105 for Rh6G obtained from previous FCS measurements,20a kISC and kT for TMR from Table 2, and the absorption cross sections, σ1n ) 0.77 × 10-17 cm2 and σT1n ) 3.85 × 10-17 cm2, of S1 and T1 determined by Thiel26 were fixed. Table 2 shows our results for four dye-specific photochemical parameters defined in Figure 1: (1) the composite microscopic bleaching rate constant, kb, of the first electronic excited states, which allows us to evaluate the classical quantum yield of photobleaching, φ3b ) 2.5 × 10-6 for Rh6G and 5.1 × 10-7 for TMR (eq 9); (2) the lifetimes, τXn1 ) 1/kXn1, of the higher electronic excited states, Xn (X ) S or T), of Analytical Chemistry, Vol. 70, No. 13, July 1, 1998

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Table 2. Photostability Properties of Rhodamine-6G (Rh6G) and Tetramethylrhodamine (TMR) in Water Obtained from FCS dye

kb (s-1)a

φ3bb

τXn1 (fs)a,c,d

kbXn (s-1)a,c

pbXnc,e

kISC (s-1)f

kT (s-1)f

Rh6G TMR

6.5 × 102 2.2 × 102

2.5 × 10-6 5.1 × 10-7

200 200

2.8 × 108 1.2 × 108

5.6 × 10-5 2.4 × 10-5

7.3 × 105 5.4 × 105

3.9 × 105 4.0 × 105

a These values were obtained from fitting eq 12 to the measured values of k b 3 c z,av(I0/2) obtained from FCS (Figure 5A,B). φb ) kb/k0 (eq 9). X ) S or T. d τXn1 ) 1/kXn1. e pbXn ) kbXn/(kXn1 + kbXn) (eq A3). f kISC and kT were determined from FCS (eq 19). Their standard deviation is in the 5 -1 5 -1 25b 6 -1 5 -1 20a ref ref ref ref order of 40%. Reference values in the case of Rh6G: kISC ) 4 × 10 s , kT ) 3 × 10 s ; kISC ) 1.1 × 10 s , kT ) 4.9 × 10 s ; kISCref ) 7.5 × 105 s-1, kTref ) 2 × 105 s-1 (solvent: ethylene glycol).26

Figure 5. Irradiance dependence of the phenomenological bleaching rate constant, kz,av(I0/2), (b) determined from the measured FCS curves for Rh6G (3 × 10-10 M in water) (A) and TMR (10-9 M in water) (B) using eq 19. The data are well described by the five-level model (eq 12) (full curve) and do not fit to the three-level model (eq 8) (dashed curve). Fixed fit parameters: Rh6G (A), k0 ) 2.56 × 108 s-1, σ01 ) 2.22 × 10-16 cm2, kISC ) 1.1 × 106 s-1, kT ) 4.9 × 105 s-1; three-level model, kb ) 310 s-1 (Table 1); TMR (B), k0 ) 4.35 × 108 s-1, σ01 ) 1.33 × 10-16 cm2, kISC ) 5.4 × 105 s-1, kT ) 4.0 × 105 s-1; three-level model, kb ) 140 s-1 (Table 1); both dyes, σ1n ) 0.77 × 10-17 cm2, σT1n ) 3.85 × 10-17 cm2). For variable fit-parameters, see Table 2. (C) Dependence of the probability of photobleaching, pb, on the excitation irradiance, I0/2, calculated (eq 13) for both dyes (full curves) using the above parameters. For comparison, the probability of photobleaching, p3b, obtained from the cellbleaching method is given (b) (e.g., P ) 2 W at focal diameter of 2.5 mm). (D) The calculated mean number of emitted fluorescence photons, NF(I0/2), from a single Rh6G molecule (eq 20) using the above parameters and Φf ) 0.98 for several mean transit times, tt, through the detection volume. (Inset of D) The signal-to-background ratio, F/B(I0/2), of a single-molecule experiment using Rh6G is obtained from (1) the calculated detected fluorescence count rate, F ) gANF/tt, of a single molecule transit (values of NF from D), assuming a detection efficiency of gA ) 3% of the setup and (2) the background count rate, B ) 0.49tt1.5I ∼ VI (V ∼ ω03 ∼ tt1.5, applying a constant ratio z0/ω0). The unit of the factor 0.49 is Hz cm2/W ms, which has been determined from a measurement using a CW argon ion laser (514.5 nm) at an epi-illuminated microscope (ω0 ) 0.5 µm, z0/ω0 ) 5, transit time of a single Rh6G molecule was tt ) 0.27 ms).

approximately 200 fs; (3) the bleaching constants, kbXn, of the higher excited electronic states, Xn (X ) S or T), which cannot be obtained separately; and (4) the computed probability, pbXn ) kbXn/kXn1, of photobleaching in Xn (X ) S or T) (eq A3, Supporting Information). 2658 Analytical Chemistry, Vol. 70, No. 13, July 1, 1998

It is obvious that two totally different experimental techniques, cell-bleaching and FCS, yield similar values for the bleaching parameters φ3b and kb for both dyes (Tables 1 and 2). The slight difference indicates that the extrapolation of the FCS measurements to low irradiances introduces some uncertainty. Neverthe-

less, these results indicate that the photobleaching yields of rhodamines have a nonlinear irradiance dependence and are nearly a factor 5-10 more stable at irradiances I < 103 W/cm2. This is demonstrated in Figure 5C, where the obtained dye-specific parameters kb, kbXn, and τXn1 have been used to plot the probability of photobleaching, p5p(I0/2), as a function of the excitation irradiance, I0/2, for Rh6G and TMR (eq 13). For comparison, the value of p3b ) φ3b resulting from the cell-bleaching experiment is also shown (b, Figure 5C). It is evident that a five-level system is necessary to describe the experimental data over the full range of irradiances, while a three-level system is adequate for measurements at low irradiances, where pb ) φ3b remains constant. This is in agreement with the previous definition of the two-step threshold irradiance, I2step, which can be calculated to I2step ) 5.6 × 104 W/cm2 for Rh6G and I2step ) 5.9 × 104 W/cm2 for TMR. Previous work on the photostability of Rh6G reports higher values of φ3b (up to φ3b ) 2.5 × 10-5)16a-f than very recent results obtained at low irradiances by us (φ3b ) 1.2 × 10-6, Table 1) and by others (φ3b ) 2.5 × 10-6).16g The above conclusions indicate that recent bleaching constants have not been measured at or have not been sufficiently extrapolated to low irradiances. Obviously, additional photobleaching by two-step excitation occurs due to the high irradiance used in a confocal microscope for SMD, even with CW excitation in the visible spectral range. Using pulsed excitation, this two-step photolysis has been shown to become severe with increasing pulse energies and repetition rates for coumarins in aqueous solution.9 Consequences for SMD. Conditions for SMD can be optimized with respect to the number of collected fluorescence photons and to the signal-to background ratio for a given mean transit time, tt, of a dye molecule through the detection volume (tt ) (4/3)ω02/4D).1a The mean number of emitted photons, NF, from a single dye molecule may easily be calculated by using eq 20, taking into account both saturation and photobleaching (Φf is the fluorescence quantum yield of the dye).10b For increasing sizes

NF(I0/2) )

Φf pb(I0/2)

(1 - exp(-ttkz,av(I0/2)))

(20)

of the detection volume, indicated by increasing mean transit times, tt, the dependence of the average number, NF(I0/2), of emitted fluorescence photons on the irradiance, I0/2, shows three characteristic features. These features are illustrated in Figure 5D, taking the dye Rhodamine 6G as a typical example (thin lines): (1) NF has linear dependence for low irradiances; (2) saturation mainly determines the maximum values of NF for short transit times, tt, as shown by comparison with calculated data disregarding photobleaching (bold lines); and (3) the increased probability of photobleaching at high irradiances is only relevant for longer transit times, tt. This becomes evident from the considerable shift of the maximum values of NF toward lower irradiances and from the increased difference from the calculated

curve disregarding photobleaching (bold line). However, for SMD, there is a trade-off between NF and the signal-to-background ratio, F/B (inset of Figure 5D).4b,8,10 The size of the applicable detection volume and, hence, the number of collected fluorescence photons is limited by the background signal, which is proportional to the detection volume and to the irradiance. If, for example, a signal-to-background ratio of 10 is sufficient for measurements using Rh6G, an irradiance of 2.5 × 105 W/cm2 and a detection volume with tt ) 1 ms will give the highest signal count rate. CONCLUSION The goal of this work was to define the optimal conditions for laser-induced fluorescence detection of several laser dyes, taking photobleaching into account. A closed description of the photobleaching behavior and its dependence on the excitation irradiance based on a five-level molecular electronic state model regarding two-step photolysis is given. The model presented can explain the strong dependence of the quantum yield of photobleaching, φb, on the excitation irradiance. At low irradiances, when twostep excitation can be neglected, φb was found to be much lower than previously reported. From the results, one can conclude that the sensitivity of a SMD experiment can be improved by varying the excitation wavelength to decrease the absorption to higher excited electronic states and, thus, to suppress two-step photolysis. In the case of Coumarin 120, this could already be established by using coherent two-photon excitation at 700 nm, which opened up the possibility to detect and even identify single coumarin-120 molecules.8 Nevertheless, it may be best to choose the wavelength of maximum absorption of the S0-S1 transition, since the background signal is proportional to the excitation irradiance and a maximum absorption would require the lowest excitation irradiance to obtain a certain fluorescence signal. At present, experiments are underway to extend this study to the influence of oxygen and additives on the photostability of dyes at high excitation irradiances. ACKNOWLEDGMENT We are grateful to J. Troe and J. Wolfrum for generous support of this work. We thank E. Elson for stimulating discussions. This work was supported by the Bundesministerium fu¨r Bildung und Forschung, Grant 0310806. SUPPORTING INFORMATION AVAILABLE Appendix A, describing photobleaching from higher electronic excited states, and Appendix B, describing the fluorescence autocorrelation function regarding diffusion, triplet population, and photobleaching (3 pages). Ordering information is given on any current masthead page. Received for review January 7, 1998. Accepted March 24, 1998. AC980027P

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