Biophysical Journal 84:588-598 (2003)
© 2003 The Biophysical Society
Two-Photon Thermal Bleaching of Single Fluorescent Molecules
Giuseppe Chirico*,
Fabio Cannone*,
Giancarlo Baldini* and
Alberto Diaspro
* Istituto Nazionale per la Fisica della Materia, U.d.R. Milano-Bicocca, Via Cozzi 52, 20126, Milan, Italy and Instituto Nazionale per la Fisica della Materia, U.d.R. Genova, Via Dodecaneso 33, 16146, Genoa, Italy
Correspondence: Address reprint requests to Giuseppe Chirico, Dept. of Physics, University of Milan-Bicocca, 20126 Milan, Italy. Tel: 39-02-64482872; Fax: 39-02-64482894; E-mail: giuseppe.chirico{at}mib.infn.it.
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ABSTRACT
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We have studied the fluorescence emission by two-photon excitation of four dyes widely used for bioimaging studies, rhodamine 6G, fluorescein, pyrene and indo-1 at the single molecule level. The single dye molecules, spread on a glass substrate by spin coating, show a constant fluorescence output until a sudden transition to a dark state very close to the background. The bleaching time that is found to vary in the series pyrene, indo-1, fluorescein and rhodamine 6G from the fastest to the slowest one respectively, has a Gaussian distribution indicating that the observed behavior is not due to photobleaching. Moreover, the bleaching time decreases with the glass substrate temperature reaching a vanishing nonmeasurable value for a limiting temperature whose value is found in the same series as for the bleaching time, from the lowest to the highest temperature respectively. The observed bleaching shows a clear correlation to the amount of absorbed power not reirradiated as fluorescence and to the complexity of the molecule. These observations are interpreted as thermal bleaching where the temperature increase is induced by the two-photon absorption of the single dyes as confirmed also by numerical simulations.
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INTRODUCTION
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Single molecule spectroscopy requires often the immobilization of the molecules onto solid substrates and the use of relatively high excitation intensity obtained through single photon confocal microscopy (Garcia-Parajo et al., 2000
; Lu and Xie, 1997; Pierce et al., 1997; Xu and Young, 1988) or two-photon excitation microscopy (Sanchez et al., 1997; Chirico et al., 2001). Single molecule spectroscopy is generally characterized by blinking due to the intersystem crossing (Veerman et al., 1999; Garcia-Parajo et al., 2000) or the conversion to differently protonated states (Weber et al., 1999; Zumbusch and Jung, 2000). The on-off switching of blinking typically occurs in the time scale of milliseconds (Garcia-Parajo et al., 2000). For single photon excitation, the sudden irreversible loss of fluorescence from single molecules was ascribed tentatively either to photo- or thermally induced bleaching. On the other hand, although two-photon excitation has several advantages for the spectroscopic and imaging applications (Denk et al., 1990; Diaspro, 2002), little is known about similar effects on the stability of the molecules. The studies in the literature mostly refer to bulk measurements. Mertz (1998) has compared the single to two-photon excitations with particular regard to the saturation or higher levels transitions. More recently a work by Patterson and Piston (2000) has provided data on bulk solutions of dyes that indicate an enhanced photobleaching in two-photon spectroscopy due probably to a three-photon process.
Several definitions of bleaching can be given (Song et al., 1995; 1996), and we can envision two main sources. The molecule may convert from the excited state, usually with a radiative decay constant in the tens of nanoseconds range, to a second excited metastable state with vanishing radiative constant. Irreversible photobleaching and blinking are usually ascribed to this type of transition. Another possibility is that the molecule changes its structure in such a way that the molecular ground state assumes a vanishing cross section for the excitation light. This modification may be induced by isomerization or thermal absorption. In both cases the molecular fluorescence emission drops to zero.
It is the primary aim of the present work to assess the effect of two-photon excitation on the total amount of fluorescence that can be collected from a single immobilized molecule at the high excitation intensities required for single molecule studies with two-photon excitation. To this purpose we have considered four dyes, namely: indo-1, rhodamine 6G, fluorescein, and pyrene. For these molecules we have evaluated the total amount of fluorescence light that can be recovered from each dye versus the excitation intensity, the temperature, the duration, and the nature of the excitation. The choice of these dyes is motivated also by the different complexity of the chemical structure that increases from pyrene to indo-1. The main result of this research is the characterization of the thermally induced bleaching of the dyes and a clear correlation of the bleaching time and its dependence on the excitation intensity, with the photophysics parameters of the molecules. These conclusions will be based also on numerical simulations of the local temperature increase during laser excitation.
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MATERIALS AND METHODS
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Optical setup
The laser source is a mode-locked Ti:sapphire laser (Tsunami 3960, Spectra Physics, Mountain View, CA) pumped by a solid state laser at 532 nm (Millennia V, Spectra Physics) that produces pulses with 
100 fs full-width at half maximum (FWHM) at a repetition frequency of 80 MHz and has an average power output 700 mW at 
= 770 nm. The optical setup is built around an inverted microscope (TE300, Nikon, Firenze, Italy) and a PCM2000 Nikon scanning head. A portion of the laser beam is focused at the entrance of the PCM2000 by a plano-convex lens with a numerical aperture of 0.15, passes through a dichroic mirror (650 DCSPRX C72-38; Chroma Inc., Brattleboro, VT) and is sent to the entrance pupil of the objective (N.A. = 1.4, Plan Apochromat 100X oil, Nikon, Firenze, Italy) by the scanning lens. The laser power at the object plane can be adjusted by means of neutral filters; we estimate that 30% of the laser light entering the scanning head is actually exciting the sample due to losses and absorption of the light mainly in the objective. The fluorescence signal, collected by the same objective and selected by a filter (HQ535-50, Chroma Inc., Brattleboro, VT), is fed to a multimode fiber that brings the light to a photomultiplier (R928, Hamamatsu, Milan, Italy) in the PCM2000 controller (Diaspro, 2001).
Sample preparation
The rhodamine 6G solutions have been prepared by dissolving rhodamine 6G (Fluka Chemika, Milan, Italy, Cat. No. 83698) in dimethylsulfoxide (DMSO) at a concentration 100 µM. The fluoresceine solutions have been prepared by dissolving fluoresceine (Fluka Chemika, Cat. No. 46955) in TRIS buffer at a concentration 100 µM. The glass slides are spin coated with solutions obtained by diluting the DMSO-rhodamine and the TRIS-fluoresceine concentrated stocks in ethanol at concentrations 70–300 nM. The Pyrene solutions have been prepared by dissolving pyrene powder (Fluka Chemika, Cat. No. 82650) in DMSO at a concentration 100 µM. The Indo-1 solutions have been prepared by dissolving Indo-1 powder (Fluka Chemika, Cat.No. 57180) in MilliQ water (Millipore S.p.a., Milano, Italy).
Glass slides cleaning
The glass slides have been soaked first in a 1% sodium dodicyl-sulfate (for 24 h), then in a saturated methanol solution of NaOH (for 2 h). We have then employed a two-step protocol to remove NaOH. We first soaked the slides in a 0.1% HCl solution for 2 h and then in diluted chromic solution (KCr2 in concentrated phosphoric acid) for 2 h. The glasses were then stored in ethanol and finally rinsed thoroughly with MilliQ water (Millipore S.p.a., Milano, Italy) and dried with nitrogen flow just before the fluorescent solutions were spread on the glass slide by spin coating.
Imaging of the slides
The fluorescence emitted from the slides is imaged by the Nikon EZ-2000 software interfaced to the PCM2000 scanning head (Diaspro et al., 2001). The point spread function of the setup has been measured elsewhere and corresponds to a plane resolution of 0.21 µm and an axial resolution of 0.7 µm (Diaspro et al., 1999). The acquisition of the images (160 x 160 pixels) with residence times in the range 9.6 µs per pixel takes 0.24 s. The field of view employed is in the range 10–15 µm and the excitation power is usually 15–45 mW at the entrance of the scanning head, unless otherwise explicitly stated. With our estimate that only 30% of the laser light actually impinges on the sample, the light intensity is 1000–3000 kW/cm2. We report the estimated values of the power at the sample in the results. The temperature of the slides is kept at the desired temperature by thermostating a copper ring at contact with the cover slip. Most of the measurements have been performed at room temperature, T 21.0°C. The images were taken by exciting at the wavelengths = 770 nm for rhodamine 6G and fluorescein, and = 720 nm for pyrene and indo-1.
Fluorescence kinetics of the spots
We have taken sequential images for a total time of 100 s. The fluorescence intensity of each spot has been computed by summing the pixel content in a circular area around each spot and by normalizing for the number of pixels in this area that have a typical diameter of 10 pixels. The maximum illumination time per spot is therefore 1 ms for a residence time 9.6 µs, and can be estimated from the time needed to scan an area of 10 x 10 pixels on the 160 x 160 image. The time per image is 229 ms and corresponds to the time interval between the subsequent illumination of each molecule. The data reported in the Results section have been shown versus the time interval between subsequent images.
The stability of the microscope stage in the z-direction has been assessed by taking two 140 x 140 µm2 images right before and after the kinetics on a 10–15 µm field of view, and by verifying that only the spot on which the kinetics was performed was missing in the second 140 x 140 µm2 image. We checked also for the stability of the acquisition module (Hamamatsu photomultipliers, R928), by imaging a DC-biased green light emitting diode and performing long-term kinetics as done for the studies of the dyes. The stability of the signal was found to be 0.4% on a 100 s kinetics.
The computation of the total intensity of a spot is made by means of home-coded MathLab (Mathworks, Torino, Italy) programs that allow also to identify a single spot on a time series of images and to compute the spot intensity versus the acquisition time (Chirico et al., 2001).
Fluorescence histograms on images
Single snapshot images showed typically several distinct spots ascribed to fluorescence signal from either single dyes or small aggregates (Fig. 1). To assess the aggregation number of each spot a histogram analysis of the fluorescence output was performed on the first image of each fluorescence kinetics series. We always obtained histograms with discrete peaks corresponding to a fluorescence output linearly spaced and indicating the presence of aggregates of different order. A typical result is shown in Fig. 1.
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RESULTS
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Fluorescence kinetics versus the excitation power: single molecules
Before investigating the fluorescence kinetics we studied the trend of the fluorescence signal per single molecule versus the average excitation power, 
P
ave. All the data, collected between 3.4 and 13.4 mW are always well described by a second power law, as shown in Fig. 2. The best fit to a law of the kind 
gives the values of AEXC reported in Table 1.
We have then followed the fluorescence emission of several (80) single dyes and small aggregates at different excitation intensities. For single dyes the fluorescence remains relatively constant until a sudden drop to a value very close to the background level from the glass slide occurs (Fig. 3). The time at which the transition occurs is evaluated by fitting the fluorescence output to a sigmoid function and by taking the middle transition time, TB. The bleaching rate, 
B, defined as the inverse of this time, has a distribution very close to a Gaussian with a small width (typically 6%; see the inset of Fig. 3). This clearly indicates that the process leading to the loss of fluorescence is not photobleaching, because an exponential distribution should be found in this case (Garcia-Parajo et al., 2000; Veerman et al., 1999). On the other hand, the observed bleaching does depend on the excitation power, Pave, as shown in Fig. 4 for all the four dyes investigated. The trend of the data is well described by a power law of the type, 
and the values of the best fit parameters are reported in Table 1. The value of the power exponent is found in the range 2.1 < C < 2.6 in the series pyrene < Indo-1 < fluorescein < rhodamine.
Fluorescence kinetics versus the excitation power: aggregates
When following the fluorescence kinetics of the aggregates we found a multistep decrease of the signal as shown in Fig. 5. The number of steps was consistent with the aggregation order as evaluated from the histogram analysis (for an aggregate of order N we observed a number of fluorescence drops 
N). Moreover the fluorescence drop per step was always very close to the quantum of fluorescence per molecule measured on the histograms. The bleaching times tN,n of an aggregate of order N were defined as the time corresponding to the nth drop of fluorescence signal. For each aggregate and excitation power, we found that the average value 
lies very close to TB. By forcing the fit of the fluorescence kinetics for the aggregates to a single exponential decay, 
, we obtained an average time decay constant, 
N, which is approximately linearly dependent on the aggregation number 
(see inset of Fig. 5). The slopes 0 for the four dyes at P = 10 mW are reported in Table 1.
Recovery of the fluorescence after bleaching
For rhodamine 6G, fluorescein, and indo-1, we found that a percentage (see Table 1) of the single molecules investigated, recovered the fluorescence signal after the bleaching as shown in Fig. 3. For pyrene, no recovery after bleaching was observed for the samples and the observation times employed here. The time span when no fluorescence signal was observed, TD, was found slightly dependent on the excitation power (data not shown) and the average values are TD = 34 ± 2 s for fluorescein, TD = 43 ± 3 s for rhodamine 6G and TD = 59 ± 3 s for indo-1. The percentage of the molecules that showed a recovery after bleaching showed a marked dependence on the excitation power as shown in the lower inset of Fig. 3. Within the time window of our acquisitions, we observed a second bleaching of the recovered fluorescence signal after a time TDB, that depends on the excitation power. The corresponding bleaching rate, 
, was found close to B within 10%, at most (data not shown).
Fluorescence kinetics with intermittent excitation
The observed dependence of the bleaching rates on the excitation power could be related to the integral of the absorbed power or to the way the molecules are illuminated. To discriminate between these two possibilities, we studied the fluorescence kinetics from single dyes with intermittent excitation. Three fluorescence images were collected from the sample for a total illumination of 
I = 3 x 229 ms and then the laser light was blocked for a variable interval 
after which the sample was again imaged for I. This illumination sequence was repeated for a total acquisition time > 100 s (see Fig. 6). As observed in Fig. 6 for the example of rhodamine 6G, the emission of fluorescence continued up to a time TB*. This behavior was found for all the four dyes. We computed an effective bleaching time, 
, as the total time for which the molecules were illuminated and emitting: 
. For each dye TBR increases with D and the data are well described by a linear law (see Fig. 6, right panel), TBR = AR + BR*D, where AR is found close to TB = 1/B (within 10%), and BR varies accordingly to the molecule as reported in Table 1.
Fluorescence kinetics versus substrate temperature
The dependence of the bleaching time on the duration of the intervening dark periods may suggest an absorption effect that could lead to a temperature increase of the sample or the substrate. If this occurs, the fluorescence kinetics should be dependent on the substrate temperature. Therefore the time kinetics of the single dyes was followed versus the substrate temperature for different values of the excitation power. As reported in Fig. 7 the bleaching time was found to decrease versus the temperature with a slope that depends on the excitation power. Moreover, the bleaching time was found for each dye to intersect the temperature axis at a definite value of temperature T0, approximately independent of the excitation powers investigated (see Fig. 7). The average values of T0 taken over the sets of excitation powers are: T0 = 64.6 ± 1.8°C for rhodamine 6G, T0 = 40.7 ± 3°C for fluorescein and T0 = 26.4 ± 0.5°C for indo-1. The fast bleaching of pyrene at room temperature did not allow to study its temperature dependence.
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FIGURE 7 Bleaching times versus the substrate temperature for: indo-1 (top panel, excitation powers 10, 8.4, 7.8 mW from the bottom to the top curve); fluorescein (middle panel, excitation powers 11.7, 10, 8.4, 5.7 mW from the bottom to the top curve); rhodamine 6G (bottom panel, excitation powers 13.4, 10.7, 9.7, 7.8 mW from the bottom to the top curve).
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DISCUSSION
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In the measurements reported here, we observed fluorescence spots that can be ascribed to the emission from single molecules or small aggregates according to the histogram analysis reported in the Materials and Methods section and in Fig. 1. The dependence of the single molecule fluorescence output on the square of the excitation power indicates (see Fig. 2) that a two-photon excitation is taking place. No evidence for saturation effects was detected for the dyes investigated here indicating that the two-photon saturation power must be larger than 10 mW corresponding to 
3000 kW/cm2 similarly to the data reported by Brand et al. (1997) on coumarin-120 in solution. Because the saturation intensity for pulsed excitation (with pulse width much less than excited state lifetime) is proportional to 
we can estimate an intensity saturation of 14,000 kW/cm2 for a typical two-photon cross section of 
2 = 50 GM and a laser pulse width p = 100 fs. This saturation value is 4–5 times larger than the maximum intensity reached here. On the other hand the absence of saturation evidence in the data reported in Fig. 2 may indicate that the cross sections of the investigated dyes, when on glass, is lower than in solution. The emission of fluorescence from single molecules or small aggregates fluctuates around an average value until a single or multistep drop to the background level as shown in Fig. 3.
Before making considerations on the fluorescence kinetics, we have checked that the reported behavior does not depend on the optical setup. The stability of the microscope stage in the z-direction and the stability of the acquisition module were assessed as described in the Materials and Methods section. We considered also molecular diffusion or sublimation as a possible explanation of the fluorescence loss, alternative to the changes in the photophysical parameters of the molecules. However this does not seem to be the case (Wahl, 1996) because the molecules were immobilized on the surface of the glass by physisorption and similar results as those reported here were found on samples sealed with a glass slide on the top (data not shown). The observed photobleaching is not even due to artifacts related to the saturation of the ground state because the fluorescence intensity dependence on the excitation power is very well described by a quadratic law (see Fig. 2). The saturation is ruled by the excited state lifetime of the dyes on the glass substrate that is probably shorter than that measurable in the bulk solutions. By assuming an average lifetime 1 ns for the dyes, we can estimate that our experiments have been carried out with intensities about an order of magnitude below the saturation level. Likewise, any significant variation of the 150-fs pulse-width as a function of power would also affect the fluorescence signal producing a discrepancy with the square law dependence.
A few observations can then be made on the fluorescence kinetics of the type reported in Fig. 3. First of all, the process leading to the loss of fluorescence is neither photobleaching nor blinking, because an exponential distribution of the off times (and on times) should be found for a stochastic process, while the distributions of the TB that we recover from the data were very close to a Gaussian function (see inset in Fig. 3). This distribution of the bleaching times indicates that the phenomenon is not ruled by stochastic processes, such as the transition between excited electronic states.
Moreover the fluorescence emission is not continuous but interrupted by long dark intervals: in some cases the fluorescence is recovered within the 100 s observation window (see Fig. 3 and lower inset therein). The lifetime of the triplet state varies from few µs to tens of ms (Veerman et al., 1999), while the length of the dark periods observed by us is on the order of seconds. On the other hand the blinking due to the triplet-singlet interconversion (Dickson et al., 1997; Zumbusch and Jung, 2000; Song et al., 1996; Haupts et al., 1998; Schwille et al., 2000) is masked in our 250 ms acquisition time. Instead, our finding of emission intervals separated by dark periods suggests the existence of an additional (nonemissive) state B in the usual three-levels electronic system, S0 (singlet ground state), S1 (singlet excited state) and T1 (triplet ground state). The state B might be characterized by a low two-photon cross section for the wavelengths used here, 720 nm–770 nm, or by a vanishing quantum yield.
On the basis of the results on the temperature dependence of the bleaching (see Fig. 7), we suggest that the silent state B may be related to a thermally induced structural change of the dyes. As indicated also by Walser et al. (2001) with line width and line shift measurements at cryogenic temperatures, one part of the laser power is absorbed by the single molecules and dissipated to the substrate. Within this hypothesis the common temperature value T0, to which the curves of the bleaching time versus the substrate temperature are converging, should be closely related to the value at which the single dye undergoes the structural transition to the state B. For pyrene it was not possible to collect bleaching data at temperatures significantly higher than 21°C, room temperature, because the bleaching was rapidly increasing to a level where no fluorescence from single molecules could be collected.
Also the loss and recovery of fluorescence can be cast in this thermally induced transition picture if we assume that the B state is characterized by a very low cross section for the infrared (IR) radiation. In this case, the dark time should be the time needed for the molecule to lower the temperature and undergo a transition to the original S0 state. As a partial check to this hypothesis we notice that the dark times, TD, depends very little on the excitation power, typically <10% (data not shown). On the other hand the percentage of the molecules that recover fluorescence after TD, decreases with the excitation power (see inset in Fig. 3) and this indicates that not all the molecules in the B state can find a way back to the S0 state when the temperature reaches the initial value.
This thermal bleaching hypothesis must be compared to the theoretical predictions of the sample temperature increase. The previous estimates given in the literature for the temperature increase due to two-photon excitation microscopy experiments (Schönle and Hell, 1998; Denk et al., 1995), dealt with the very weak water single-photon absorption which corresponds to the first order cross section for water at 720–800 nm and is of the order of 10-24 cm2, almost eight orders of magnitudes less than the resonant single-photon cross section for dyes in the visible. In a conventional two-photon excitation imaging the fluorescent labels are slowly diffusing through the excitation volume and the environment has a relatively high thermal conductivity (
water). Therefore the temperature increase of the dye environment due to the two-photon absorption of the fluorophore is negligible (Schönle and Hell, 1998). However in experiments on single molecules immobilized on glass surfaces the molecule is continuously illuminated and a percentage of the absorbed power is dissipated into heat. We assume for simplicity that all the nonradiative deexcitation processes lead to an increase of the thermal vibrations, therefore the temperature increase should be proportional to (1 - 
), where is the quantum yield. As a matter of fact the energy loss due to the vibrational relaxation occurring in the excited state leads to an additional molecule temperature increase which should then be proportional to but we assume here that this contribution is negligible. The thermal dissipation occurs both in the air and in the glass slide in a way that is difficult to model. Because the thermal conductivity of glass is almost 100 times larger than that of air, we can estimate an upper and lower bound to the temperature increase, by computing it for the case in which the molecule dissipates either completely in air or in glass. Moreover the molecule is somehow hydrated because the measurements are not taken in dry air. This increases the effective size of the molecule that can be considered in any case as a point absorber of the laser power. To make an estimate, we suppose therefore that the molecule is located at the beam waist of the laser beam and that the thermal conductivity of the medium is uniform. The temperature increase, 
T(r, t), satisfies the diffusion equation:
 | (1) |
where 
is the mass density and CP is the specific heat at constant pressure of the molecule (in cal/g°K). The source term, f(r, t), is the absorbed power per unit volume per laser pulse, that can be written for a two-photon absorption as:
 | (2) |
where 2 is the two-photon cross section of the molecule, Pave is the average power, i(r) is the normalized laser power profile and b(t) is the time profile of the laser pulse. We assume that the laser pulses have a width of p 200 fs and the laser repetition is 
L = 80 MHz. For a single photon excitation the source term is:
 | (3) |
where 1 is the single photon excitation. This can be the case of the hydration water layer excited by the IR radiation. The solution of the diffusion Eq. 1 for the two-photon absorption can be obtained by applying the Fourier transform as reported in the Appendix and Eq. 10 can be easily employed to perform a simulation of the effective increase in the local temperature. Because the contribution of CP and of the single hydrated dyes is small, we can simulate the temperature increase by assuming the density and the specific heat of water and the thermal conductivity either of the air, air = 6 x 10-6 Kcal/sm°K, or of the glass, glass = 10-4 Kcal/sm°K.
Moreover, because the computations made above assume a three-dimensional Gaussian shape for the laser beam in the focus, we take 
and 
, that gives an excitation volume close to that of our two-photon setup. The simulations have been performed for a dye with a two-photon cross section 2 = 50 GM (1 GM = 10-50 cm4 s/photons) and a quantum yield = 0.5 illuminated with an average power Pave = 10 mW. The results, shown in Fig. 8 indicate that, at least under the simplifying assumption that the heat dissipation occurs completely in air, the temperature increase is relatively high and comparable to the limit values of the temperatures T0 (see Fig. 7) below which fluorescence can be observed. The heat relaxation times for air and glass are xy 1 µs and xy 0.015 µs, respectively. However the curves in Fig. 8 are well described for t > 1 s by an exponential growth, with a characteristic time 10 s (see solid line in Fig. 8). Because it is difficult to model the interactions of the molecule with the glass substrate, we can imagine that the actual increase in the temperature lies between the two extremes obtained for the dissipation in air or in water. In any case we could predict an increase of several degrees in the local temperature depending on the excitation power and the quantum yield. Fig. 8 shows that the temperature increases rapidly toward an asymptotic value at high temperature. This finding, compared to the experimental values of the bleaching time that can reach several tens of seconds, may suggest that the transition to the putative dark state does not occur right after the molecule has reached a threshold temperature and that the molecular structure needs some finite time to make the transition to the new electronic dark state after exploring different conformational states.
According to the thermal bleaching model, after the molecule drops into a dark state where its cross section is much lower than in the initial ground state, the temperature decreases with time according to Eq. 8 because then no heat is absorbed. Obviously this assumption is an oversimplification because the so-called dark state may still absorb light but with much lower two-photon cross section that implies that the local temperature increases at a much lower rate. On the other hand the heat diffusion times, xy or z, are of the order of microseconds or even less and therefore the local temperature must decrease to room temperature very rapidly. This prediction would be inconsistent with the observed dark times TD 30–40 s, if we simply assumed that TD is the time needed to the molecule to reach a lower temperature at which it can convert back to the ground state S0. One possible explanation for this behavior is that, for the B-S0 conversion to take place, the molecule must reach a lower temperature and then a finite time is required to explore the possible conformational states. Moreover the hydration shell continuously absorbs IR radiation, although to a very limited extent because 1 10-24 cm2 (Hale and Querry, 1976), and this may hinder and slow down the heat dissipation of the molecule even after the transition to the dark state B has occurred. A simple simulation gives a maximum increase in the temperature of 1.6°C for an average excitation power Pave = 50 mW and 0.3°C for Pave = 10 mW, as shown in the inset of Fig. 8. This tiny increase in temperature of the hydration water is probably not large enough to induce a reduced heat diffusion time, xy and z, from the molecule. On the other hand a further indication that the cooling relaxation time C is of the order of a few seconds comes from an analysis of the fluorescence kinetics observed under intermittent illumination. If we assume an exponential growth of the local temperature with warming up time W, followed by a hyperbolic relaxation as indicated by Eq. 8, we can predict a temperature increase after n illumination cycles (of duration D + I):
 | (11) |
where 
and 
are the room temperature and the limiting temperature reached upon warming up, respectively. The number of cycles n* needed to reach the value of the temperature that allows the molecule to make the transition to the B state, must be proportional then to the ratio 
, and the bleaching time 
. The increase of with D is therefore:
 | (12) |
where we have assumed that I << W, which seems to be the case because I 0.6 s and W 10 s (see fit in Fig. 8). Because BR varies in the range 0.2–3 for the four dyes, we can infer that the cooling time is of the order of the warming time, i.e., lies approximately in the range 0.1–10 s. Apart from the above suggestions, we have no direct and simple explanation for such a long cooling time as can be inferred from the analysis of our data.
The simulations reported above for the temperature increase of the molecule and the hydration water can help understanding the behavior of the thermal bleaching at different substrate temperature for all the dyes. The higher is the starting substrate temperature, the lower is the local temperature jump that must be made for the molecule to fall into the B state. In particular for pyrene, for which the limiting temperature, T0, seems to be very close to the room temperature, 21°C, any small increase of the local temperature, such as that predicted for the water shell, would be enough to bring the molecule into the B state or to keep it from a conversion back from the B to the S0 ground state. This is also in agreement with the fact that for pyrene we could not observe, at room temperature, any fluorescence recovery after the first thermal bleaching (on a sample of 80 molecules) because the local environment is probably at T > T0 due to the water absorption alone. We believe that although on a semiquantitative basis, these theoretical considerations indicate that the thermal bleaching hypothesis with a 
transition is compatible with the physical-chemical parameters of the two-photon absorption of the dyes.
We expect therefore to find a common description of these observations by considering the amount of IR light absorbed that is not radiated back. This quantity must be proportional to the product of the single molecule cross section immobilized on the glass surface, 
, times the fraction of the absorbed photon pairs that are not converted in fluorescence photons. This second parameter is given by 1 - , where is the quantum yield. We assume here that the quantum yield of the excited singlet state of the four dyes is the same as that obtained by single photon excitation and reported in the literature (see Table 1). On the other hand, the two-photon cross section of the single molecules, , cannot be inferred from the literature data that report bulk measurements in solution and we must rely on the fluorescence response to the excitation power determined on the single molecules on the substrates. Because the parameter 
, retrieved from the square law fit of the data taken on single molecules, is proportional to 
, we take the product 
as a measure of the amount of the excitation power that is not radiated back as fluorescence by single dyes on the glass slides. The values of 
are reported in Fig. 9 below the structure of each dye. The bleaching of the dyes observed here is correlated to in many ways. First, the best fit curvature, B, of the bleaching rate increases with while the exponent, C, decreases (see Fig. 9). The behavior shown by B can be ascribed to a faster increase of the bleaching with Pave for those dyes that dissipate less radiative energy. The analysis of the trend of the exponent C, that varies in the range 2.1–2.6, is more delicate. The raw data would suggest that the process involves more than two photons for rhodamine 6G, because C 3, while for pyrene only two photons are needed. Similar observations have been reported by Patterson and Piston (2000) for two-photon bleaching of fluorescein and indo-1 on microdroplets immobilized between glass slides. The authors reported a somewhat steeper dependence of the bleaching rate upon the excitation power with an exponent 3. They ascribed tentatively this behavior to a sequential excitation of the dye in the excited state by a third photon as also indicated for rhodamines by Widengren and Rigler (1996) and Sanchez et al. (1997). However the data reported by Patterson and Piston (2000) could not definitely confirm this model and the authors indicate the possibility of higher resonance absorption.
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FIGURE 9 Correlation plot of the best fit parameters with the amount of excitation power not reradiated, . Upper panel: Left axis, % of the fluorescence recovery at 10 mW; right axis, slope BR of the bleaching time upon intermittent illumination, TBR, versus the dark time D (see Fig. 6); middle panel: left axis, slope of the bleaching times of small aggregates versus the aggregation order (see text), 0; right axis, temperature T0 at which no fluorescence can be detected (see Fig. 7); lower panel: left axis, bleaching rate amplitude, B; right axis, bleaching rate exponent, C. The bleaching rate was fit to the law . In all the panels, the lines are exponential fits intended only to guide the eye. The chemical structures and the values of for the four dyes are reported on the side and below the graphs.
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Also the percentage of the recovery of the fluorescence signal depends monotonically on (Fig. 9, upper panel). The observed decrease indicates that an efficient conversion of the excitation power into molecular vibrations leads to dark states so far from the ground state S0 that it is difficult for the molecule to retrieve it. This observation supports therefore the existence of a family of dark states. Finally the slope, BR, of the bleaching time versus the dark time in the intermittent illumination experiments (Fig. 9, upper panel) is found to decrease with . From the analysis of the temperature increase upon intermittent illumination reported above (see Eqs. 11 and 12) it is clear that the increase of the TBR with D is the more efficient the smaller is the rate of increase of the local temperature of the molecule, i.e., 1/W, that is by definition related to the parameter . Finally we notice from Fig. 9 that the parameter does not parallel the complexity of the chemical structure. We try here to define the complexity of the dyes in connection to their possibility to undergo a structural transition. Pyrene is the most rigid structure among those investigated here. Fluorescein and rhodamine 6G are very similar with a rigid structure composed of three condensed rings connected to a benzene ring by a simple C-C bond that allows certain degrees of rotation. Moreover rhodamine 6G has further rotational degrees of freedom in the alkyl groups CH3CH2- e CH3-. These two dyes are characterized by very similar values, 0.5–0.9, which are much lower than that of pyrene, 3.7. However for indo-1, whose structure is by far the most complex being characterized by an indole group and two benzene rings connected by simple bonds around which the rotation is allowed, we compute 2.3. Therefore the chemical structure alone can hardly help in predicting the bleaching property of the dyes. Moreover the good description of the data in terms of the fraction of the absorbed power not going into radiative processes, , appears to support our assumption that the contribution of the vibrational relaxation occurring in the excited state is negligible.
The kinetics of the aggregates call for a separate set of considerations. The multistep decay of the fluorescence is a further indication of the single molecule level of the present measurements. The spread in the bleaching times within each aggregate is definitely larger than the width of the Gaussian distribution found for the single molecules. This fact suggests that the excitation power absorbed by the molecules is not equally distributed over molecular vibrations in the aggregate. Molecules in the aggregate may easily show a different quantum yield due to molecular interactions that opens new deexcitation channels. Therefore the observed spread might be due to slightly different values of for the different monomers in the aggregates. This also correlates with the finding that the spread in the bleaching times in an aggregate increases with the number of aggregation. The larger the number of monomers, the larger is the number of possible interactions that lead to slightly different values of .
|
CONCLUSIONS
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|---|
We have presented some evidence that two-photon excitation bleaching at the high excitation intensities needed for single molecule experiments is due to thermal effects. The main cause might be an increase of the local temperature due to the two-photon absorption of the molecules that, being in air, cannot easily dissipate the absorbed heat. The molecular parameter that seems to rule this phenomenon is the amount of absorbed power that is not reradiated as computed on the molecules adsorbed on the glass substrates. These observations shed some light on the bleaching induced by two-photon excitation in single molecule experiments when the molecules are trapped onto solid matrices or three-dimensional structures (e.g., gels). Moreover these data suggest that to increase the number of fluorescence photons per single molecule upon two-photon excitation hydrated samples are more convenient because they can more easily dissipate the thermal loads. Preliminary results on labeled proteins on glass surfaces, in wet silica gels and in trehalose glasses indicate an increase in the thermal bleaching time from the glass surfaces to the wet environment. We suggest therefore that the reduced observation window for single molecules upon two-photon excitation is linked more to the dissipation channels of the absorbed power of the excited molecules rather than to the immobilization on solid substrates. Immobilization procedures, such as wet silica gels, that allow to confine the molecules and to control the hydration of the molecules might therefore be preferable for these types of studies. This systematic study should therefore be extended to different trapping media of interest in single molecule basic research and applications, such as silica or polyacrylamide gels. Finally the observed behavior and the correlations found with the molecular chemical and physical parameters, may be of some help for the design of molecules with switching on-off behavior of longer duration.
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APPENDIX
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The solution of the diffusion Eq.1 for the two-photon absorption can be obtained by applying the Fourier transform as:
 | (4) |
whose integral is:
 | (5) |
At the time scale of interest here (>> 1 µs) we can assume the laser pulse to be of vanishing width, 
, and obtain:
 | (6) |
The temperature increase of the molecule can be estimated at r = 0, i.e., at the beam waist, as:
 | (7) |
When the laser first impinges on the sample, the term 
. The laser profile is described by a Gaussian-Lorentzian function, however for the sake of simplification of the computation we assume the laser profile to be approximated by a three-dimensional Gaussian, 
. The Fourier transform of i(x,y,z) is 
and the molecule temperature drop, after each laser shot, can be approximated as:
 | (8) |
where 
and 
.
However, because during each image recording the molecule is illuminated for approximately TON = 960 µs or equivalently for approximately M = 16,000 shots, the overall temperature increase during the illumination period is:
 | (9) |
After the illumination period of TON 960 µs, the molecule is kept in darkness until the next image occurring after Timage 230 ms, approximately. This implies that the molecular temperature relaxes according to the time dependence of Eq. 8 for each image and for the total acquisition time, Timage = M * 0.23 s, we obtain:
 | (10) |
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ACKNOWLEDGEMENTS
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This work was partially supported by grants from the Istituto Nazionale per la Fisica della Materia, Pais SinPhys for the year 2002. We are indebted to Cristiano Viappiani for helpful discussions.
Submitted on May 16, 2002;
accepted for publication July 10, 2002.
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TOP
ABSTRACT
INTRODUCTION
), Rhodamine 6G (•), Pyrene (
), and Indo-1 (
). The data are fit to a law of the type 
. The parameter AEXC is reported in 
; the best fit values of B and C are reported in 
(
. The best fit parameter BR is reported in 