Two-color fluorescence correlation spectroscopy of one chromophore: Application tothe E222Q mutant of the green fluorescent proteinG. Jung, C. Bräuchle, and A. Zumbusch Citation: The Journal of Chemical Physics 114, 3149 (2001); doi: 10.1063/1.1342014 View online: http://dx.doi.org/10.1063/1.1342014 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/114/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Protein dynamics from single-molecule fluorescence intensity correlation functions J. Chem. Phys. 131, 095102 (2009); 10.1063/1.3212597 Mechanical perturbation-induced fluorescence change of green fluorescent protein Appl. Phys. Lett. 86, 043901 (2005); 10.1063/1.1856142 Gas-phase absorption properties of a green fluorescent protein-mutant chromophore: The W7 clone J. Chem. Phys. 119, 338 (2003); 10.1063/1.1542880 Single-molecule optical spectroscopy of autofluorescent proteins J. Chem. Phys. 117, 10925 (2002); 10.1063/1.1521150 Green fluorescent proteins as optically controllable elements in bioelectronics Appl. Phys. Lett. 79, 3353 (2001); 10.1063/1.1419047

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Two-color fluorescence correlation spectroscopy of one chromophore:Application to the E222Q mutant of the green fluorescent protein

G. Jung, C. Brauchle, and A. Zumbuscha)

Department Chemie, LS fu¨r Physikalische Chemie, and Center for Nanoscience, Ludwig-MaximiliansUniversitat Munchen, Butenandtstr. 11, D-81377 Mu¨nchen, Germany

~Received 17 July 2000; accepted 28 November 2000!

Fluorescence correlation spectroscopy~FCS! is an important method for investigations of diffusionprocesses as well as of photophysical properties of fluorescing molecules. It has lately been appliedin studies of the photodynamics of the green fluorescent protein~GFP!. In this case FCS yieldsvaluable information about the population of dark, non-fluorescing states of the molecule. Forthree-level systems rate constants into and out of the dark state can easily be determined with FCS.This task however becomes significantly more complex for molecules that possess several darkstates. Here we present two-color FCS with simultaneous two-color excitation as a method that alsoyields spectroscopic information about the dark states. This makes the complete analysis of amolecular four-level system possible. The analysis of the GFP mutant E222Q is given as an exampleof two-color FCS that is readily applicable to other molecules with photoconvertible dark states. ForE222Q we determine all the rate constants within the four-level system. With these data wecalculate the population of the different molecular states in bulk experiments as encountered, e.g.,in microscopic studies. ©2001 American Institute of Physics.@DOI: 10.1063/1.1342014#

I. INTRODUCTION

Lately the green fluorescent protein~GFP! of the jelly-fish Aequorea victoriahas become one of the most importantfluorescent labels in molecular biology. It is currently theonly protein that can be expressed in prokaryotic as well asin eukaryotic cells and which fluoresces without the additionof external cofactors.1 Its widespread applicability led to aquest for new mutants of GFP with altered spectroscopicproperties.2 However any specific mutation aimed at produc-ing a desired spectroscopic change obviously affords an in-timate knowledge of the protein’s basic photophysics. Forthis reason many spectroscopic investigations of GFP haverecently been performed. In the course of investigations ofdifferent GFP mutants we developed a new technique basedon the well established fluorescence correlation spectroscopy~FCS!. This technique employs simultaneous two-color exci-tation of one chromophore. In this paper we present the com-plete analysis of results from measurements of the GFP mu-tant E222Q as an example of the scope of the method that webelieve to be useful for investigations of a broad range offluorescing molecules.

The active chromophore in GFP is 4-~p-hydroxy-benzylidene!imidazolidin-5-one3 which is formed in a post-translational reaction. In the properly folded protein the chro-mophore is protected by a barrel like structure composed ofb-strands.4,5 The absorption spectrum of wt-GFP has aprominent double absorption peak in the visible region cen-tered at 400 nm and 475 nm as shown in Fig. 1. Upon exci-tation at either of these wavelengths fluorescence emissionnear 510 nm is observed. The origin of the peculiar emissionproperties of wt-GFP was determined using ultrafast pump–

probe spectroscopy.6,7 Deuteration experiments show that thelarge Stokes-shift after excitation at 400 nm is due to excitedstate proton transfer of a tyrosine in the neutral chro-mophore. After excitation the tyrosine is deprotonated withina few ps and mainly red-shifted fluorescence from the an-ionic chromophore is observed. At room temperature thisemission is spectrally not distinguishable from emission after475 nm excitation.

Low-temperature high resolution fluorescence spectros-copy however reveals that this emission does not originatefrom the state absorbing at 475 nm but from an intermediatestate.8–10This intermediate state can be rationalized as a pro-tein containing an anionic chromophore with its local envi-ronment not yet relaxed to accommodate the anionic insteadof the neutral chromophore. After emission of a photon theprotein will most likely return to its initial ground state con-taining the neutral chromophore. It was possible to determinethe barrier heights connecting the different states on the po-tential energy surface with temperature dependent measure-ments.8

Unfortunately no rate constants for transitions betweenthe different states accessible to GFP can be derived fromlow-temperature fluorescence spectroscopy of GFP. In prin-ciple they can be obtained from time-resolved measurementslike the pump–probe techniques mentioned above. Withthese however only states populated with sufficiently largerates are observable, while states with small population rateconstants and comparatively long lifetimes, as e.g. tripletstates, are hard to analyze. In this case fluorescence correla-tion spectroscopy~FCS! offers an alternative for investiga-tions of photodynamics on a time scale from 100 ns to 1ms.11 FCS experiments with different mutants of GFP havebeen performed by several groups12–14 and several darka!Author to whom correspondence should be addressed.

JOURNAL OF CHEMICAL PHYSICS VOLUME 114, NUMBER 7 15 FEBRUARY 2001

31490021-9606/2001/114(7)/3149/8/$18.00 © 2001 American Institute of Physics

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states have been detected. An important advantage of theFCS technique is that the experiments can be performed un-der quasi native conditions or even in intact cells.15 Intensitydependent andpH dependent measurements near neutralpHshow that one of the dark states of GFP can be attributed toan external protonation process, a behavior that is expectedfor an indicator base. It remains however difficult to clearlyattribute the dark states observed at higherpH values to dis-tinct dynamical processes as all spectroscopic informationabout the nature of these states is missing.

In analogy to pump–probe techniques we therefore re-cently proposed a two-color FCS experiment. Here bothspectral and dynamical information can be extracted throughthe spectral separation of the exciting beam and a probingbeam. In our setup a second beam is used to probe the spec-tral properties of one dark state of a molecule.16 Our methodis different from previously described cross-correlationFCS17 by the fact that only one chromophore is present. Theexperimental scheme is based on the fact that in many caseselectronic absorption by the dark states can be expected tolead to a repopulation of the initial emitting state. Thesechanges will manifest themselves in the fluorescence emis-sion dynamics that are monitored with FCS. In the workmentioned above we exploited the fact that for the GFP mu-tant E222Q it was possible to depopulate one of the darkstates with a second color illumination. Thereby we effi-ciently created a molecular three-level system, the transitionrate constants of which are easily determined.11 We werethen able to estimate rate constants for transitions into andout of the second dark state. Instead of this approximatesolution this paper will describe the complete analysis of themolecular four-level system of E222Q in which special em-phasis is laid on the second wavelength dependent process.This analysis will lend itself also to cases where a completedepopulation of the dark state with a second illuminationsource is not possible. We want to use this as an example forthe possibilities offered by our two-color FCS scheme thatreadily lends itself to applications with other dyes possessing

photoconvertible dark states.18 We show how the rate con-stants that we derive can be used to explain the publisheddata for two-color bulk saturation experiments16 and that it ispossible to calculate effective population numbers for theinvolved dark states.

II. METHODS AND MATERIALS

The setup employed here is based on a homebuilt con-focal microscope as used in single molecule experiments.Light from a Kr1- and an Ar1-ion laser~Coherent Innova200 and Innova 90-5! is simultaneously focused onto thesample using a dichroic mirror~Chroma, 485 DCXR! and aNikon 60x, NA 1.2 water immersion objective on an invertedNikon TE 300 microscope. Both beams are combined andmade collinear using a dichroic beamsplitter~Omega420DCLP02!. The distance of the centers of the beams waschecked in a separate imaging experiment to be smaller than150 nm. Note that a good overlap is crucial for the reproduc-ibility of the experimental data. Emitted light is collectedwith the same lens and directed through a confocal pinhole~diameter 50mm or 100mm! at the back focal plane of themicroscope. Remaining excitation light is removed withbandpass filters~Omega, 535DF55, or Chroma, HQ 510/50!.For bulk experiments the signal is then detected with a singleavalanche photodiode~EG&G Canada, SPCM-AQR-14!connected to a photon counting system~Stanford Research,SR400!. For FCS experiments the signal is split up using a50/50 beamsplitter before being fed in two separate ava-lanche photodiode modules. This procedure circumventsproblems that might arise due to afterpulsing of the APDsand extends the accessible time scale to the sub-msregion.11,19 The autocorrelation functions were recorded us-ing a commercial correlator~ALV Langen, ALV-5000/F!.Samples of the E222Q GFP mutant were obtained from Wie-hler and Steipe from the Genzentrum Mu¨nchen. In this spe-cific mutant, the H-bonding framework that stabilizes theneutral form of the chromophore is interrupted by replacingglutamic acid at position 222 by glutamine.20 Absorption andfluorescence excitation spectra do not show any populationof the neutral state of the chromophore atpH values used inour experiments. Figure 1 shows the absorption maximum ofE222Q centered at 475 nm. The emission maximum is de-tected at 506 nm and the fluorescence quantum yield is esti-mated to be 50%. We determined the fluorescence lifetime ofE222Q with a F900 fluorescence spectrometer from Edin-burgh Instruments. The protein solutions were diluted to thesingle molecule detection limit (531029 M) using 20 mMbuffer solution ~Fluka, pH 10, HPCE grade! and air-saturated water~Sigma, HPLC grade! for the FCS experi-ments. Bulk measurements were performed with 1027 M so-lutions. We checked thepH dependence of our bulksaturation data and found no influence ofpH on these in therange frompH 6 to pH 10. For the FCS experiments thehigh pH was chosen to exclude any possibility of an externalprotonation of the protein which facilitates the analysis of thedata. For the fitting procedure we used the Origin 6.0 soft-ware ~Microcal!. Up to ten curves for different intensitieswere globally fitted. Six fitting parameters were used, four ofwhich were independently determined. Two parameters

FIG. 1. Absorption spectrum of wild-type GFP atpH 7 ~dotted line! and theGFP mutant E222Q atpH 10 ~solid line!. Excitation at either of the shownabsorption bands leads to fluorescence emission centered at 508 nm for thewild-type GFP and 506 nm for E222Q. The inset depicts the neutral and theanionic form of the chromophore, respectively.

3150 J. Chem. Phys., Vol. 114, No. 7, 15 February 2001 Jung, Brauchle, and Zumbusch

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which were not influenced by the second color illuminationwere restricted to having the same value in all ten curves.The error margins indicated below result from error propa-gation.

III. THEORETICAL BACKGROUND

FCS was introduced in the early 1970’s21 as a method toinvestigate intensity fluctuations in liquid samples. The the-oretical background of the method was worked out by Elsonand Madge.22 In brief FCS measures the autocorrelationfunction g(2)(t) of the emission from fluorescing moleculesin a dilute solution. The probability to detect a photon at atime t after an initial emission event is governed by intramo-lecular processes, which lead to the population of nonemis-sive dark states, as well as by diffusion of molecules into andout of the small detection volume. With the term dark statesmentioned above we either refer to other electronic states ofthe same molecule like, e.g., triplet states or to photoproductswith different absorption and emission properties. After atransition into the dark state the molecules are in both casesusually not excited anymore by the wavelength applied in theexperiments.

In the visible spectral region, the photophysics of allGFP mutants is determined by an equilibrium between theneutral and the anionic state of its chromophores. Their rela-tive stability and, to a smaller extent, the absolute position oftheir absorption and emission bands is determined by theexact nature of the protein scaffold. Tsien classifies mutantsthat exhibit no absorption attributable to the presence of aneutral chromophore in their ground state as class II or classIV mutants.2 There is however experimental evidence thateven for these mutants the neutral state of the chromophorecan play an important role in the excited state dynamics.23 Inthe case of the GFP mutant E222Q, two-color bulk saturationexperiments lead us to the conclusion that two dark states arepresent in this molecule.16 These are the putative triplet stateand a state of the protein containing the neutral chro-mophore. Consequently the photodynamics of E222Q haveto be modeled with a four-level scheme as depicted in Fig. 2.The rate equations then have the following form:

d

dt S @S0#

@S1#

@T#

@RH#

D 5S 2k12 k21 k31 k41

k12 2k212k232k24 0 0

0 k23 2k31 0

0 k24 0 2k41effD

3S @S0#

@S1#

@T#

@RH#

D • ~3.1!

Here@S0#, @S1#, @T#, and@RH# denote the population of thesinglet ground state, of the first excited singlet state, of thetriplet state, and of the state of the protein containing a neu-tral chromophore, respectively. Rate constants between thedifferent states are given askmn .

There are four solutions of this equation system. Onecorresponds to photon antibunching which is not observableon the time scale of our experiment. A second solution isobtained for the stationary state in which case the rate equa-tions transform into a homogeneous algebraic equation sys-tem. This solution will be discussed in detail below as itallows us to calculate the population of the different molecu-lar states in bulk experiments. The remaining two solutionsl1 andl2 ~Ref. 24! can be used to determine the contrastsC1 and C2 .25 To obtain the autocorrelation functiong(2)(t) as it is observed in the FCS experiment one has tomultiply g(2)(t)511C1 exp(2l1t)1C2 exp(2l2t) with adiffusional part,12

g~2!~t !5^I ~ t !I ~ t1t!&

^I ~ t !&2

5111

N S 11t

tDD 21

3~11C1 exp~2l1t!1C2 exp~2l2t!!.

~3.2!

A two-dimensional model appropriate for our setup was con-sidered for the diffusional part. This only leads to a negli-gible error of less than 2% in the determination of diffusionaltimes for the 50mm pinhole used in our experiments.26 Thediffusional part is of no further interest in our analysis of theintramolecular photodynamics. Both the contrastsC1 andC2

and the rate constantsl1 andl2 depend on all of the transi-tion rate constantskmn in the four-level system,

C1,25~k23

eff1k24eff6S!~k23

effk41eff1k24

effk31!1~k41eff2k31!~k24

effk312k23effk41

eff!

2k31k41eff~6S!

~3.3!

FIG. 2. Schematic four-level diagram depicting the molecular energy levelsand the transition rate constants for E222Q as used in the calculations. Thestates one through four correspond to the singlet ground stateS0 , the firstexcited singlet stateS1 , the triplet stateT, and the stateRH of the proteincontaining the neutral chromophore respectively.k41

eff is introduced to ac-count for the light driven repopulation of state one.

3151J. Chem. Phys., Vol. 114, No. 7, 15 February 2001 Fluorescence correlation spectroscopy

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and

l1,2512~k311k41

eff1k23eff1k24

eff6S! ~3.4!

with

S5A~k23eff1k312k24

eff2k41eff!214k23

effk24eff. ~3.5!

The contribution of the spontaneous emissionk21 is consid-ered in the effective rate constantsk23

eff andk24eff ~cf. Fig. 2!,

k23eff5k23

k12

k121k21, k24

eff5k24

k12

k121k21, k125s12

476I 476.

~3.6!

I 476 indicates photon flux densities which is a convenient unitfor the description of molecular absorption processes. It canbe converted to kW/cm2 by multiplication with (hc/l)31019. As described above we expect level four to be aphotoproduct. In our case this photoproduct absorbs light at407 nm with an absorption cross sections41

407. Illuminationwith this wavelength leads to the repopulation of the absorb-ing state one. As it cannot be assumed thats41 vanishes atl5476 nm, an additional term at this wavelength is includedin k41

0 . We get an effective rate constant,

k41eff5k41

0 1k414075k41

therm1s41476I 4761s41

407I 407. ~3.7!

k41therm shall denote a thermally activated process. The subse-

quent analysis is greatly simplified by recognizing that

C1~ I 407,I 476!1C2~ I 407,I 476!5k23

eff

k311

k24eff

k41eff

5P1S s41407

k24eff 3I 4071

k410

k24effD 21

.

~3.8!

Thus this equation splits up into three different parts corre-sponding to intensity ratiosP(I 476)5k23

eff/k31, Q(I 476)5s41

407/k24eff , andR(I 476)5k41

0 /k24eff that lend themselves to fit-

ting procedures to the respective intensity dependent datasets. Note that none of the ratiosP, Q, R is intensity depen-dent for illumination atl5407 nm.

IV. RESULTS

For many applications GFP mutants with a stabilizedanionic chromophore and therefore only a single absorptionaround 475 nm are desirable. The E222Q mutant reportedhere also belongs to these class II mutants. Bulk experimentswith the excitation of a 531027 M solution of E222Q withan intensityI 47657.6 kW/cm2 at 476 nm accordingly lead toa strong fluorescence emission centered at 506 nm. Applica-tion of an additional low intensity illumination of less than2.5 kW/cm2 at 407 nm surprisingly leads to an overall in-crease in the total detected fluorescence count rate of 140~610!%. It was possible to prove that under the experimentalconditions chosen, two dark states are present in E222Q. Oneof these presumably is the triplet state. Even under low in-tensity illumination atl5476 nm approximately 60% of themolecules are trapped in the second dark state which absorbsat l5407 nm. It is known from other mutants that the ab-sorption maximum of the neutral chromophore is centered

around 400 nm. We therefore attribute the second observeddark state in E222Q to a state of the protein containing aneutral chromophore. The increase in fluorescence count ratewith two-color illumination was shown to be caused by anefficient repopulation of the ground state.16

In order to investigate this finding in more detail weperformed two-color FCS experiments. In Fig. 3 the influ-ence of the second color illumination atl5407 nm on theautocorrelation functions is depicted. An increase in the in-tensity I 407 clearly leads to a reduced contrast ofg(2)(t).However even for intensities corresponding to a saturation ofthe increase in fluorescence signal, some contrast remains.

Our aim here is to determine the different transition rateconstants within the four-level system from intensity depen-dent FCS measurements as shown in Fig. 2. Equation~3.8!states that the sum of the contrastsSC5C11C2 is a func-tion of I 407 and can be written as a sum of three different rateconstant ratiosP, Q, R. In a first step we therefore determineSC in dependence ofI 407. Data for two different intensitiesat 476 nm are shown in Fig. 4. The data obtained are thenfitted to a function of the form~3.8! and the different termsare analyzed separately. Compared to our previously re-ported analysis this procedure has the advantage of smallererrors and applicability even in cases where a complete re-population with an additional light source cannot beachieved. According to Eq.~3.8!, P can be obtained fromextrapolatingI 407→`. For low intensitiesI 476 we can re-write P as

P~ I 476!5k23

eff

k315

k23

k313

s12476I 476

s12476I 4761k21

'k23

k313

s12476

k213I 476. ~4.1!

We previously determinedk31523104(610%) s21.16 Us-ing an absorption cross sections12

47652.0 Å2 typical for classII mutants27 and our measured fluorescence lifetimet

FIG. 3. Two-color fluorescence correlation spectroscopy of the GFP mutantE222Q. The excitation intensities were 48 kW/cm2 at l5476 nm and variedfrom 0 to 18 kW/cm2 for l5407 nm. The lower solid line shows the part ofthe autocorrelation curves due to diffusion of the molecules out of the ex-citation volume. All curves were normalized to the same magnitude of thisdiffusional part.

3152 J. Chem. Phys., Vol. 114, No. 7, 15 February 2001 Jung, Brauchle, and Zumbusch

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51/k2152.5 ns we calculatek23 according to Eq.~4.1! andobtaink23533105(620%) s21. Within a better error limitthis is the same as our previously published value.

After having determined all the rate constants connect-ing to state three in our scheme we have to investigate therespective rate constants involving state four. This is accom-plished by analyzing the data for the two other rate constantratiosQ(I 476) andR(I 476) appearing in Eq.~3.8!. In the limitof low intensitiesI 476 the equation forQ(I 476) can be rewrit-ten as

Q~ I 476!5s41

407

k24eff 5

s41407

k243s12

476I 476

s12476I 4761k21

's41

407k21

k24s124763

1

I 476. ~4.2!

A hyperbolic fit as shown in Fig. 5 yields the prefactor on theright-hand side of Eq.~4.2!. From this we can calculate theratio s41

407/k24 using the known values fors12476 and k21 to

obtains41407/k2450.035ms Å2(630%). Knowing the prefac-

tor we can now derives41407. For low excitation intensities

I 476, Eq. ~3.4! simplifies to

2l1,25k311k23eff1k41

eff1k24eff6@~k311k23

eff!2~k41eff1k24

eff!#~4.3!

so that in the fitting procedure theI 407 dependent decay con-stant

l25k41eff1k24

eff5k410 1s41

407I 4071k24eff ~4.4!

can be used.Thuss41

407 can be determined as the slope of the sum ofthe rate constantsk24

eff1k41eff recorded for different intensities

I 407 ~data not shown!. We get s4140750.0028(630%) Å2.

From this value and Eq.~4.2! we can calculatek24583104(640%) s21.

The last remaining rate constant for the complete de-scription of the four-level system isk41

0 . To obtain a valuefor this rate constant we investigate the dependence of therate constant ratioR(I 476) from Eq. ~3.8! on the intensityI 476. Interestingly Fig. 6 shows that 1/R(I 476) does not fol-low a linear law intersecting the origin as one might haveexpected. Instead we observe a nearly constant value. Thisresult can be explained by a repopulation of the ground statethrough l5476 nm light absorption of dark state four. Asimilar behavior for other mutants was observed by otherauthors.14 For low intensitiesI 476 we can reformulate theexpression forR as

FIG. 4. Sum of the contrastsC1 andC2 for different intensitiesI 407 at twoconstant intensitiesI 476548 kW/cm2 ~upper curve! and I 476515 kW/cm2

~lower curve!. The values of the ratioP extrapolated forI 407→` are indi-cated as open squares. The intersection with the ordinate yieldsP11/R. Thesolid lines are fits to the experimental data.

FIG. 5. Values for the ratioQ in dependence of the excitation intensityI 476.s41

407 and k24 can be extracted from the hyperbolic fit to the experimentaldata~solid line!.

FIG. 6. Values for the ratio 1/R in dependence of the excitation intensityI 476. s41

476 is determined from the fit to the experimental data~solid line!.Fitting a constant to the data does not yield a different value fors41

476 withinthe error limits. Using Eq.~4.5! for the fitting procedure however lets usdetermine an upper value fork41

therm. The straight dotted line depicts thebehavior expected in the absence of repopulation due to illumination atl5476 nm.

3153J. Chem. Phys., Vol. 114, No. 7, 15 February 2001 Fluorescence correlation spectroscopy

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1

R~ I 476!5S k41

0

k24effD 21

'

k24

s12476

k21I 476

s41476I 4761k41

therm

5s24

476I 476

s41476I 4761k41

therm. ~4.5!

We get

s24476

s414765

k24

s12476

k21

s41476 5

k24s12476

s41476k21

51.3~610%!. ~4.6!

Usage of k24583104(640%) s21 yields s414765331024

(650%) Å2. Please note thats41476 is not the absorption cross

section of state four atl5476 nm but the effective crosssection for the transfer into state one. From the fit to the datain Fig. 6 we can also estimate an upper value for the thermaldepopulation rate constantk41

therm,0.002ms21.

V. DISCUSSION

The complete four-level scheme for E222Q with all de-termined transition rate constants and absorption cross sec-tions is depicted in Fig. 7. A different analysis of the dynam-ics involving state three is possible and has been describedelsewhere.16 The values determined with both methods arethe same within the error limits. From the data obtained it isdifficult to draw any conclusion about the chemical nature ofstate three. Intensity dependent measurements as well asquenching experiments would be prerequisite in order to de-termine whether state three is a triplet state. Other authorshave reported FCS data from GFP mutants with extremelyhigh excitation intensities of up to 53106 W/cm2.14 We findhowever that no FCS experiments are possible with E222Qunder these experimental conditions due to the fast pho-

tobleaching of the molecules that prohibits any interpretationof the resulting FCS curves. In addition very high illumina-tion intensities also lead to other photoreactions that are ob-servable with low rates28 rendering the interpretation of theFCS curves difficult. Quenching experiments by contrastprove futile because of the good protection of the chro-mophore by the protein scaffold.29 The assumption that statethree is a triplet state seems plausible because of its observedlifetime of 50 ms but to date no other data supporting thisinterpretation are available. The quantum yield for the tran-sition into state three is given by the ratiok23/k21'0.1%.While this value seems to be low, one has to keep in mindthat the ratiok23/k31'15 is rather large. This means thatmore than 80% of the molecules can populate level three athigh intensitiesI 476.

Other than normal FCS experiments two-color FCS ex-periments also yield spectroscopic information about the na-ture of the participating dark states. For E222Q the spectralsensitivity of the second color response at 407 nm leads us tothe conclusion that state four corresponds to the protein con-taining a neutral chromophore. Using a second color illumi-nation at 442 nm already affords four to eight times higherintensities for the saturation of the repopulation process ascompared to 407 nm illumination~data not shown!. Againwe can calculate a quantum yieldk24/k21'331024 for thetransition into state four. The quantum yield for the repopu-lation of state one from state four with illumination atl5407 nm can be estimated to bes41

407/sRH407'0.3% assum-

ing absorption cross sectionssRH407 typical for RH mutants.27

Note however thats41476 at the wavelength of the main exci-

tation source does not vanish but has a value of19s41

407. Thismeans that a certain repopulation of the initial emissive stateis also observed with one color excitation at 476 nm. In asingle color experiment with intensitiesI 476 as employed inthis work, the depopulation of level four is dominated bys41

476I 476 and not by the natural lifetimet451/k41therm in the ms

time range. In a single molecule imaging experiments thisbehavior will manifest itself as an increased blinking withboth on and off times becoming shorter for higher illumina-tion intensitiesI 476.

The solution of the rate equations for the four-level sys-tem lets us calculate the effect of the two-color illuminationin the described bulk experiments. For this purpose we usethe steady state solution of Eq.~3.2! from which we canderive expressions for the population of the four molecularstates. Here we want to focus on theS1 state as the fluoresc-ing state and the dark stateRH containing the neutral chro-mophore. We obtain

@S1#5k41

effk31s12476I 476

k41effk31~k211k231k24!1s12

476I 476~k41effk311k24k311k23k41

eff!, ~5.1!

@RH#5k24k31s12

476I 476

k41effk31~k211k231k24!1s12

476I 476~k41effk311k24k311k23k41

eff!. ~5.2!

FIG. 7. Complete four-level diagram for the GFP mutant E222Q containingall the determined rate constants and cross sections.

3154 J. Chem. Phys., Vol. 114, No. 7, 15 February 2001 Jung, Brauchle, and Zumbusch

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From Eq.~5.2! we can calculate values for the population ofthe stateRH. In a typical bulk experiment already at mod-erate illumination intensities at 476 nm 60% of the popula-tion are transfered to this dark state. Ultimately the non-vanishing cross sections41

476 also leads to a depopulation oflevel four when solely illuminating at 476 nm as it is shownin Fig. 8. The necessary high illumination intensitiesI 476 willhowever lead to a significant population of the dark statethree. The excited stateS1 , from which fluorescence emis-sion occurs, will therefore not be significantly higher popu-lated.

To calculate the maximum increaseFI max in fluores-cence signal that can be obtained with an additional illumi-nation source, we use

FI max5@S1~ I 476,I →`

407 !#2@S1#~ I 476!

@S1#~ I 476!

5k24

k41therm1s41

476I 4763s12

476I 476

k211S k23

k3111Ds12

476I 476

.

~5.3!

It is obvious from Eq.~5.3! that at high intensitiesI 476 thefluorescence increase obtainable with a simultaneous secondcolor illumination drops hyperbolically, whereas at low in-tensitiesI 476 a linear increase can be observed. Calculatedvalues and results from bulk measurements are shown in Fig.9.

The usual problem encountered in an analysis of four-level systems as the one described here consists in the mix-ing of transition rate constants in the coefficients of the ex-ponential functions in Eq.~3.2!. For small excitation

intensities approximate solutions including transition rateconstants for only one dark state in the exponents are pos-sible. To test the validity of this approximation we comparedsuch a solution to the results obtained with the exact solu-tion. We find that the approximate solution yields values fork24 ands41

476 that are 30% higher while the value obtained fork41

therm was much too high.

VI. CONCLUSION

In this paper we present the analysis of the photodynam-ics of the GFP mutant E222Q. A novel two-color excitationFCS setup allows us to determine all the transition rate con-stants occurring in the four-level system that has to be usedto model the influence of the two observed dark states. Weprovide evidence that one of these dark states corresponds tothe protein with a neutral chromophore. The decay time ofthe other dark state lets us assume that it is the triplet state.We show this analysis as an example for the usefulness ofour two color FCS method for experiments with fluorophoreswith multiple states that are photoconvertible. The method iscurrently applied in investigations of other GFP mutants andother fluorescing proteins as well as in investigations of fluo-rescing dyes.18

ACKNOWLEDGMENTS

This work was financed by the Deutsche Forschungsge-meinschaft, SFB 533 ‘‘Lichtinduzierte Dynamik vonBiopolymeren,’’ TP B7. We are indebted to J. Wiehler andB. Steipe for providing us with GFP mutants and to P. Ze-hetmayer and S. Mais for careful proofreading and discus-sions.

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FIG. 8. Population of the stateRH of the protein containing the neutralchromophore. The values shown are calculated using the rate constants andcross sections as given in Fig. 7. Fork24 we used the upper value obtainedwithin the error limits, as this leads to a better reproduction of the bulkexperimental data~cf. Fig. 9!. Similar calculations can be performed for allof the four molecular states~data not shown!.

FIG. 9. Fluorescence signal increaseFI max obtainable with additional sec-ond color illumination atl5407 nm at different intensitiesI 476. The solidline is calculated using the rate constants and cross sections as given in Fig.7 while the experimental data are obtained from bulk measurements.

3155J. Chem. Phys., Vol. 114, No. 7, 15 February 2001 Fluorescence correlation spectroscopy

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