Fast interactions between Rh6G and dGTP in water studied by fluorescence correlation spectroscopy

Chemical Physics ELSEVIER

Chemical Physics 216 (1997) 417-426

Fast interactions between Rh6G and dGTP in water studied by fluorescence correlation spectroscopy Jerker Widengren, Johannes Dapprich, Rudolf Rigler * Karolinska Institute, Dept. of Medical Biophysics, MBB, 171 77 Stockholm, Sweden

Received 17 October 1996

Abstract The feasibility of fluorescence correlation spectroscopy (FCS) for the monitoring of fast kinetic processes has been investigated. The interaction between Rh6G and different nucleotides in water served as a model system. Following the fluorescence fluctuations arising due to dye-nucleotide interactions around an unperturbed equilibrium it is possible to retrieve information about association and dissociation kinetics of the different electronic states involved in the fluorescence generation. No macroscopic perturbation of thermodynamic parameters, as in chemical relaxation experiments, is needed. Compared to other fluorescence techniques used to study interactions of this kind, such as flash photolysis, FCS requires a very simple instrumentation. A very broad time interval can be covered and the fact that FCS is based on a fluorescence microscope allows for kinetic studies on a microscopic scale. Hence, FCS can be used in parallel or as an alternative to more established fluorescence techniques providing a simple and easy-to-use tool by which similar and complementary information on kinetic processes can be obtained. Keywords: Fluorescencecorrelation spectroscopy (FCS); Rhodamine 6G (Rh6G); Dye-nucleotide interactions

1. Introduction The mechanisms of interaction of polycyclic aromatic hydrocarbons (PAHs) and DNA are of interest for a number of reasons. Many PAHs may act as mutagens and carcinogens, binding covalently as well as non-covalently to nucleic acids. Nucleic acid base-specific quenching of dyes may be exploited as a way of fingerprinting bases in biochemistry and, with the possibility to detect single fluorophore molecules, can be used as a possible strategy for D N A sequencing [1 ] as well as provide information about the immediate surrounding of the dye and the conformation of the DNA. Previous investigations of P A H - n u c l e o t i d e interactions have involved different osmometric and sound absorption techniques [2,3]. Fluorescence is another sensitive analytical tool for detecting adducts in native DNA and for studying physicochemical interactions between PAH molecules and D N A bases. By the use of transient and steady state absorption spectroscopy, fluorescence lifetime measurements and spectrophotometry, much information can be obtained about D N A - d y e interactions.

* Corresponding author. 0301-0104/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PII S0301-0104(97)00014- l

J. Widengren et al. / Chemical Physics 216 (1997) 417-426

418

Here, data will be presented showing how fluorescence correlation spectroscopy (FCS) may serve as a complementary technique to the established ones for the investigation of dye-nucleotide complex formation, quenching of dyes by nucleotides and for DNA conformational studies. We investigated how dye-nucleotide interactions between free nucleotides and dyes in solution reflect themselves in terms of fluorescence fluctuations and to what extent information about these interactions can be obtained from FCS measurements. The fluorescence of Rh6G in water with varying concentrations of dGTP, dUTP, dATP and dTTP was studied.

2. Method, materials and experimental set-up In FCS, which was developed in the early seventies, the fluorescence intensity fluctuations from fluorescent molecules are analyzed [4-6]. Our experimental set-up has been described elsewhere [7-10]. Introducing a very small detection volume, defined from the dimensions of the focused laser beam and the collection efficiency function of the confocal microscope, and with the access to highly selective band-pass filters a very high spatial and spectral discrimination has been reached. In this way it has been possible to reduce signal-to-noise ratios considerably compared to early FCS experiments and measurement times have been shortened drastically [11]. Here, Rhodamine 6G molecules (Lambda Physik) in bidistilled water with varying concentrations of deoxynucleotides (Pharmacia) are excited by a strongly focused beam of an argon ion laser (514 nm wavelength) under a microscope objective (Zeiss Plan-Neofluar 63 × NA 1.2, water immersion cover glass corrected). The fluorescence is collected by the same objective and in a confocal arrangement passed through a pinhole (diameter 50 ~m). In order to discriminate fluorescence from laser light scattered at the excitation wavelength and from Raman scattered light of the water molecules, a band-pass filter is used (Omega Optics 565DF50). The fluorescence light is divided by a beam-splitter and detected by two avalanche photodiodes ( E G & G Model SPCM-100). The photocurrents of the two diodes are analyzed in terms of their fluctuations by a cross correlation function:

(ll(t)12(t+7)) G(7) =

(It)(12)

=

([(I)+~ll(t)][(l)+812(t+~')]) (1,)(12)

(~lt(t)~12(t+'c)) = 1+

(I,)(12)

(1)

Here, It(t) and 12(t) signify the detected fluorescence intensity and (1 l) and (/2) denote the mean values of the detected intensities in the first and second detector, respectively. By use of two detectors all inherent noise due to the detectors alone can be eliminated as long as it is not correlated between the detectors. Of special importance is that the dead time of the detectors (250 ns) can be circumvented in this way. If the fluorescence fluctuations arise due to translational diffusion in and out of the sample volume element, which is defined by the dimensions of the Gaussian-shaped laser focus and the collection efficiency function in the confocal set-up, the time dependent part of the correlation function will take the form [11,12]:

l( G°(~') = N

, 1 + 4D~'/~o~

)(

, 1 + 4D~-/o)~

"

(2)

Here, ~o~ and ~o2 are the distances from the centre of the laser beam focus in the radial and axial direction, respectively, at which the collected fluorescence intensity has dropped by a factor of e 2 compared to its peak value. N is the mean number of fluorescent molecules within the sample volume element and D is the diffusion constant of the fluorescent molecules. Eq. (2) assumes the collected fluorescence to be Gaussian-shaped in the axial as well as in the radial direction but will under our conditions also provide a good approximation for the case of a Lorentzian-shaped axial profile of the focused laser beam [7]. For the fluorescence decay measurements a mode-locked cavity-dumped Rh6G dye laser was used emitting at 560 nm with a pulse frequency of 3.8 MHz [131.

J. Widengren et al. / Chemical Physics 216 (1997) 417-426

419

3. Results and discussion Out of the nucleotides studied (dGTP, dATP, dCTP and dTTP) it was found that the presence of dGTP caused a significant change in the fluorescence correlation functions of Rh6G in water (Fig. 1). Four distinct dynamic processes could be identified from the correlation curves. They are due to (1) antibunching caused by transitions (excitation and deexcitation) between the ground and the excited singlet state of the Rh6G molecules (approximately 5 ns) [14,15]; (2) dGTP specific interactions (approximately 50 ns); (3) singlet-triplet interactions (txs) [8,10]; (4) translational diffusion in and out of the sample volume element (approximately 50 ixs). The typical time ranges for each of the processes are given within brackets. Disregarding the fastest process due to antibunching the experimental curve can be fitted to a two-exponential function superimposed onto the correlation function arising as a result of translational diffusion, Go(z): G(r)

= Go(r)[1

- T-

+ C e - ~ / ' c ] + 1.

C + Te -'/'T

(3)

The first exponential, characterized by T and r r, is caused by singlet-triplet interactions in the Rh6G molecules [8,10]. The second exponential, described by C and r c, is due to an effect specific for dGTP and will be the subject of our further investigation. The quenching of a number of different polynuclear aromatic dye fluorophores by different DNA bases is believed to involve electron transfer mechanisms if the redox potentials are of the appropriate relative magnitudes [ 16]. By means of redox potentials the quenching efficiency of photoinduced electron transfer can be predicted. Among the nucleotides, guanosine is known to be most readily oxidized, and quenching by electron transfer should for Rh6G only be possible by this nucleotide (generating a Rh6G radical anion and a guanosine cation) [17]. For rhodamine dyes, their hydrophobic nature promotes aggregate formation and likewise aggregation of rhodamine molecules with other hydrophobic compounds, like nucleotides, can be observed. Upon aggregation with guanosine quenching results from a redox reaction between the rhodamine dye and the guanosine, promoted by the proximity between the molecules and the matching redox potentials, whereby the guanosine acts as an electron donor and the rhodamine as an electron acceptor [18]. Based on these observations, a rate scheme as outlined in Fig. 2 can be set up. A similar rate scheme can be used for d y e - D N A base interactions in water in general [19] and has been used to model the interactions between DNA bases and pyrene [20,21], methylene blue [22,23] and coumarin dyes [17]. The electron transfer reactions are assumed to take place upon hydrophobic complex formation and be fast enough for the hydrophobic interaction to be the rate-limiting process.

i "

, dGTP 2 mM, Power 0.84 mW

1.1

'¢T

'

10

,..i

........

i

........

0.00001 o.oool

i

.......

o.ool

a

o.ol

........

J

o.1

........

i

1

........

i

lo

.

,,

,,,,,I

,

loo

time (ms)

Fig. I. Fluorescencecorrelation curve of Rh6G in water with 2 mM dGTP added. Here T and ~'r denote the amplitude and relaxation time of the correlation curve which is due to singlet-triplet interactions. C and ~'c are caused by interaction with dGTP. Changing Rh6G to tetramethyl-rhodamine or dGTP to dGMP did not produce any significant difference in the correlation curves. The initial rise in the correlation curve is due to antibunching.

420

J. Widengren et al./ Chemical Physics 216 (1997) 417-426

Rh6G-dGTP kdissl kc12 [

kassl

Rh6G S1

!k12

kasso

S0

Fig. 2. Kinetic scheme of the different states involved in the photophysicalprocess of Rh6G in water in the presence of dGTP. Measurements made by time-correlated single photon counting supported the observations made in the FCS measurements. For dGTP a dynamic as well as a static quenching, indicated by the presence of a two-exponential decay, could be measured. The other nucleotides only showed a very weak dynamic quenching. In the case of dGTP the fast exponential had a decay time of about 170 ps, compared to the intrinsic fluorescence decay time of Rhodamine 6G measured to be 3.9 ns. Assuming that the fluorescence quantum yield scales with the decay time, the fluorescence intensity will be strongly diminished upon complex formation. In our FCS measurements, an excitation wavelength of 514 nm was used in combination with a band-pass filter (centered at 565 nm) matching the fluorescence of the free dye. This means the excitation wavelength is somewhat shorter than the peak of the absorption spectrum. The fact that there is usually a slight red-shift in the absorption as well as in the emission spectra when rhodamine-nucleotide complexes are formed [18] will make the decrease in detected fluorescence upon complex formation even more pronounced. Therefore, in the evaluation of the FCS experiments the complex can be considered non-fluorescent. To simplify the treatment of the above kinetic scheme, we assume the decay rates of the complex as well as those of the free dye to be much faster than any of the rates related to nucleotide interactions or to singlet-triplet transitions. This simplified kinetic scheme is depicted in Fig. 3. Since the decay rate of the R h 6 G - d G T P complex was of the order 6 × 109 s - i, the excited state of the complex can be assumed to be depopulated before any considerable dissociation via kdissI could occur and will be very weakly populated. The dissociation of the complexed dye can consequently be considered to take place altogether over the ground state. The excitation intensity dependence of the association rate from the singlet states and the intersystem crossing to the triplet state from the excited singlet state, respectively, can be expressed as:

ktass = kl2/( kl2 "}- k2, ) kassl + k21/( k,2 + k21 ) kassO,

(4a)

kls c = k , 2 / ( k,2 + k2, ) k,s c .

(4b)

Regarding the triplet state of Rh6G as well as the dye-nucleotide complex as non-fluorescent, the time development of the fluorescence will follow that of the excited singlet state, given by S~(t) = k j2/(k~2 + k zj)g(t), where S(t) = So(t) + Sj(t) is the fraction of fluorophores being in either the ground or the excited singlet state. Generally, the detected fluorescence is given by 1(t) = f C E F ( r ) c(r, t)k21 qS,(r, t) dV.

(5)

Here, q accounts for the quantum efficiency of the detectors, fluorescence quantum yield of the fluorophore as well as attenuation of the fluorescence in the passage from the sample volume to the detector areas, CEF(7) is

Rh6G-dGTP

Rh6G

C Fig. 3. Simplified kinetic scheme used in the treatment of the time dependence of fluorescence intensity.

J. Widengren et al. / Chemical Physics 216 (1997) 417-426

421

the collection efficiency function of the confocal microscope set-up and c(7, t) denotes the concentration of fluorophores. The fluorescence fluctuations will be caused by changes in the excited singlet state population and concentration changes due to translational motion of the fluorophores in and out of the sample volume element. These fluctuations can be considered independent of each other. By making the assumption that the S 1 fluctuations take place on a time scale much faster than those due to translational diffusion [8,10], one may treat the S~ fluctuations separately. The normalized fluorescence correlation function, including the fluctuations due to singlet-triplet transitions, association-dissociation to dGTP and translational diffusion, can now be expressed as~

G ( ~ ) = ( l( t ) I ( t + ~ . ) 5 / ( I 5 2

= ([ + BID(t) + B/S, (t)][(I> + BlD(t + ~) + 81s,(t + ~ ' ) ] > / < I ) 2 = [ < 8 1 0 ( t ) 8 1 o ( t + r ) > + 2 + 1

= G o ( r ) + Gs,(Z ) + 1.

(6)

Since the transitions between the singlet states take place on a time scale much faster than any of the other dynamic processes, the S o and $1 states will for the longer time ranges of these processes not be resolved and can therefore be regarded as one entity, that of S (see Fig. 3). In the following treatment of the S ~ fluctuations it is for simplicity assumed that the excitation intensity is uniform over the sample volume element (a more rigorous treatment can be made following that of [10]). For the same reason, effects of complex formation on the diffusion properties have been disregarded (see Ref. [24] for a more general treatment). In order to find the expression for Gs,(~-) the following system of coupled first order linear differential equations is set up from the simplified kinetic scheme of Fig. 3:

dt

- - ( k l s C -J- ktass )

k31

kdiss0

kls C

-k31

0

k~s

0

-- kdiss 0

C

(7)

The correlation function expresses the probability of a photon emission at a time ~- given a photon emission at time 0. Now considering a fluorophore at a fixed position being subject to a constant excitation intensity, this probability will be proportional to S(-c), which is obtained from the solution of Eq. (7) with the boundary condition:

T(0)

c(0)

=

0

(8)

0

This condition simply states that after a fluorescence photon has been emitted, the fluorophore will be in its ground singlet state. S(z) can now be expressed as: 3 S(T) = E [ Aivi(1)e*"], (9) i= l where v i and Ai are the eigenvectors and eigenvalues of the differential equation matrix above. The eigenvalues will be: A, = 0, = - [k'isc + L , + k'ss + kd

ss0]/2

"4- ¢[k'is C "1t- k31 -{- k'ass -{- kdi~sO] 2 / 4 - [ k'.~sk3, + k'isc kdiss 0 -4- k3lkdissO] .

(10)

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J. Widengren et a l . / Chemical Physics 216 (1997) 417-426

The factors of A i are obtained from the boundary condition of Eq. (8). Together with the first components of the eigenvectors, they form the multiplicative factors to the exponential terms of S(7) as: k31 kdiss0 of

a,v~(1) -- - - ,

(lla)

A202(i ) = ( fl 4- ~r~)(k3' V/~ + 6 )/(4ofvrT),

(] Ib)

A 3 0 3 ( I ) = (/3 - Vt'T)(k3,~/~ - 6 ) / ( 4 o f v r T ) ,

(llc)

where of = k~ssk31 + k'isckdiss 0 + k31kdiss 0,

/3 = k',sc + k'a~s+ k3, - kd~,~0, t

,

2

= ( klSC + ka,,) + ( k~,,,0 + k,, )2 + 2( k'a,, -- k',SC) ( kd,,,0

k,, ) ;

t~ = k31 ( k'ass 4- kdiss 0 -- k31 -- k'lsc) "t- 2k'isckdiss o.

For a fluorophore under stationary excitation intensity the normalized correlation function caused by the S I fluctuations alone will be: <81s,(t)81s~(t + z)> (I>2

Gs,(~') =

k2,q-~lk2,q(S,(r) - E ) ( k2, q~-~l)2

(12)

where S-~= AlVt(1)kl2/(k~2 + k2j) is the steady state population of the'excited singlet state and S¿(~') = [ A,u,(1) +A2uz(1)e~2":+A3v3(l)e'~':]k,2/(kl2 +k2, ). Using these expressions, G s ( r ) can be written as:

a2.2(1)e ~ + a:~(1)e Alv,(l )

Gs,(7 ) =

~'~ (13)

For the full correlation function, using 1/A z, I / A 3 << ~'D = to~/4D, one will arrive at:

,(

G(~')=N

1 )(

l+4D'r/to~

,

),2

l + 4 D ' r / t o 22

[ l + G s ' ( Z ) ] +1

Azv2(1)eA2~ +A3v3(l)e~"]

1 ( 1 ) ( 1 ) 1 / 2 [ -- N

1 +4D~'/to 2

l(

,

-- NS"-~I 1 + 4D~'/~o~

1 +4D~'/to~

)(

1+

Atv,(I)

+ 1

, 1 + 4D~'/w~

SI(': ) + DC.

(14)

Comparing with the expression given in Eq. (3): r=Azv2(1), C = m303(l), r r = l/A2,

" r c = 1 / A 3.

(15)

Hence, each of the variables T, C, z r and r c can be expressed as functions of the rate parameters k~0, kassl , kdiss0, klsc, k31 , k21 and k~2 = trl~ c. By measuring fluorescence correlation functions at different excitation

423

J. Widengren et a l . / Chemical Physics 216 (1997) 417-426

GTP

2mM

o°.4

=,

T olo !"-, .--~....~LT.

C

°41 0.3 0.2

01

=

010

~

,

0.1

-

•

. . . .

__

. . . . . . .

__

_--i------tr

,

1

.......

'1'0

~ l - - t - - ~

,

10

31"0 ~

"CT t.~,~s,

~C (ns)

•0.1 .....

b'.~ . . . . . . . .

80 60~•

4il

•

--'-!~--11~

~

. . . . . . . .

h -

1'0

---I1~--

i

= [

2

......

i

0.1

10

Power

(roW)

Fig. 4. Outcome of a general analysis of Rh6G in an aqueous 2 mM dGTP solution at different excitation intensities. The measured values of T, C, ~'r and r c are plotted as well as their fitted values according to the expressions of Eq. (14) and Eq. (15).

intensities, Iexc, one will for each correlation curve get four experimental values of T, C, r r and z c and hence four equations for the rate parameters. In this way, an overdetermined equation system can be obtained from which the different rate constants can be extracted (Fig. 4). While the first exponential, being due to population of the triplet state, vanishes at low excitation intensities, the amplitude of the second exponential, resulting from complex formation and subsequent quenching by dGTP, only decreases slightly. This indicates that a complex formation leading to quenching takes place from the ground singlet as well as from the excited singlet state. The same evaluation procedure was repeated for several different concentrations of dGTP. In Fig. 5 the rate constants of ka~0, kassl and kdiss 0 are plotted versus the concentration of dGTP. From these plots, the quenching efficiencies from the ground as well as from the excited singlet state can be extracted and determined to be 2.4 x 10 9 and 3.8 X 10 9 M - I s - l , respectively. According to Smoluchowskis relation this corresponds to 35

30-

a

kass 1

25-

•

kassO

x

kdissO

~'~ 2o-

'~

v

15-

51

x

x

9

x

.'""" // s

-""

[] I I

. " " xr

×-/

~'"

× /

×

I

.'m

0

Conc. dGTP (raM) Fig. 5. The calculated rate constants of association from the ground and excited singlet states, kass0 and kassl, and that of dissociation, kdiss, plotted as a function of dGTP concentration.

424

J. Widengren et a l . / Chemical Physics 216 (1997) 417-426

J

0.02~ 001-1 • ~= 0.00/4

.

0 l'01

,

.

,

2

kdiss= 1.3X107S-1 kQ'=3.5xl09 M-is-t

.

,

4

.

,

6

.

|

8

10

3.03- r ° c,si 2.5 2.0 1.5

~ ' ~ -

~J~

1.0

0.5 ~ 0.0

.

o

,

.

,

2

4

;

;

;o

dGTP conc. (raM) Fig. 6. A simplifiedestimate of the associationand dissociationrate constants.The parameters of kdiss and k'ass were simultaneouslyfitted to the two curves of 1 / t r = k'ass[dG'rP]+kdiss and C / S - C/(1 - T - C) = k'ass[dGTP]/kdiss. The two parameters were determined to kdiss= 1.3× 107 S-1 and krass= 3.5× l0 9 M I s - I respectively. approximate reaction radii of 0.6 and 0.9 nm with reactions taking place in approximately every third and second d y e - d G T P collision, respectively. The dissociation rate remained more or less constant (1.5 x 107 s - I ) , as one would expect. The dissociation constants, defined as kdiss0//kassl and kdisso/kass0 for the ground and the excited singlet state are then estimated to 135 and 210 M -~, respectively. The values obtained are comparable to what has been reported for intermolecular quenching of other dyes such as benzo(a)pyrene tetraol by dG in water [21,25,26] and pyrene by dGMP [20] and are somewhat higher than what has been reported for the quenching of several rhodamine dyes by dGMP [18] as well as those reported for coumarin dyes [17]. As an alternative to the analysis outlined above a more simplified approach may be used, where only the association-dissociation kinetics of Rh6G and dGTP molecules have been considered (Fig. 6). This analysis gives estimates of k'ass and kd~ss with a reduced analysis effort. However, without considering triplet state and saturation effects. From time-correlated single photon counting measurements the rate constant for dynamic quenching, corresponding to ka, s~ in the above treatment, could be determined to be 2.8 × 109 M - J s-1, which is fairly well in agreement with the value of ka,sj obtained from the FCS measurements. As mentioned earlier, the fluorescence decay showed a two-exponential decay behaviour, indicating a static quenching as well (Fig. 7).

0.30-

dGTP quenching

0.29~ o

0.28-

0.270.260.25 "

~,

'

;

'

;

'

1'0

'

1'2

'

1'4

" 1~6

dGTP (mM) Fig. 7. Dynamic quenching of Rh6G by dGTP in water. Fluorescencedecay rate of uncomplexed Rh6G in water as a function of dGTP concentration.

J. Widengren et al. / Chemical Physics 216 (1997) 417-426 0.900.850.800.75. 0.700.650600.550.500.450.400.35.

425

[3

°

0

[ °

2

4

ktsC (106S "1)

•

k31 (106S -1)

6

8

10

dGTP conc. (mM) Fig. 8. The calculated rates of intersystem crossing and triplet decay plotted versus dGTP concentration.

The fastest decay time remained more or less constant with different dGTP concentrations (170 ps). The relative amplitude of the fast component was more pronounced than the corresponding amplitude of C = A3t;3(l) in the FCS measurements. The probable reason for this is that the excitation wavelength (560 nm) as well as the emission filter (600 nm cut-off filter) favoured the fluorescence of the complex to that of the free dye. In Fig. 8 the measured rates of intersystem crossing from the excited singlet state of the free dye to the triplet, klsc, and the rate of triplet decay to the ground singlet, k3t, a r e plotted versus dGTP concentration. While the rate of intersystem crossing remains almost unchanged, the triplet decay rate is clearly reduced. The absence of a clear influence on the intersystem crossing rate indicates that the triplet state energy level lies above that of the separated ions in the complex, so that no quenching to the triplet state takes place [27]. The intersystem crossing rates calculated here are somewhat lower than what has been reported previously [10]. This is most likely due to the simplified assumption of a uniform excitation over the sample volume element. A possible reason for the reduced rate of triplet decay is that the dyes upon complex formation will be partly shielded from oxygen. Oxygen is known to be a potent quencher of the triplet states of dyes like Rh6G. Similar effects upon hydrophobic complex formation has been reported for other dyes, like methylene blue [22,23].

4. Conclusions

The above experimental example shows that FCS offers a complementary technique to study intermolecular interactions between dyes and nucleotides. From the correlation data the dissociation rate from the complex ground state and the association rates from the ground singlet as well as from the excited singlet state can be extracted. The influence of the quencher on the triplet state can be obtained as well. The method of FCS requires a change in the fluorescence yield upon complex formation for the process to be visualized properly. Still, compared to established fluorescence techniques, like fluorescence decay measurements and transient absorption spectroscopy, the use of FCS can be motivated as a complementary or alternative technique for several reasons. (1) The concentration of dyes necessary in FCS is low enough to exclude any influence of dye self-aggregation, which might otherwise disturb the measurements. (2) In investigations using traditional fluorescence techniques the extraction of the rate parameters requires a combination of spectroscopic techniques and the instrumentation is in general more complicated than that used in FCS. With the exception of the detectors, filters and the correlator our instrumental set-up is based on standard components of relative cheapness. (3) FCS covers a very broad time interval over which dynamic processes may be monitored, in contrast to many traditional fluorescence techniques which are restricted to a few orders of magnitude. (4) The

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J. Widengren et a l . / Chemical Physics 216 (1997) 417-426

small sample volume element strongly reduces the amount of material necessary for the investigations. (5) FCS is based on a fluorescence microscope and microenvironmental studies of electron transfer can be performed in the same fashion as confocal microscopy is done. Finally, (6) in the case of flash photolysis, overlapping absorption spectra of various intermediates can sometimes be difficult to distinguish. The investigation made here can easily be more generalized for other kinds of dynamic processes. Here, only the population of the excited singlet state will give rise to fluorescence but it is straightforward also to include the fluorescence of other states in the kinetic treatment. The simplifications made here are not required for the feasibility of FCS for these kind of investigations, but serve to simplify the analysis in order to show more clearly how it can principally and successfully be used.

Acknowledgements The study has been funded by grants from the Swedish Natural Science Research Council, the Swedish Research Council for Engineering Sciences, and by a grant from the Humboldt Foundation to JD.

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