Excitation energy transport and trapping in concentrated solid solutions of flavomononucleotide

Biochimica et Biophysica Acta 1619 (2003) 201 – 208 www.bba-direct.com

Excitation energy transport and trapping in concentrated solid solutions $ of flavomononucleotide P. Bojarski a,*, L. Kulak b, H. Grajek c, G. Z˙urkowska b, A. Kamin´ska a, B. Kuklin´ski a, C. Bojarski b b

a Institute of Experimental Physics, University of Gdan´sk, 80-952 Gdan´sk, Wita Stwosza 57, Poland Department of Technical Physics and Applied Mathematics, Technical University of Gdan´sk, 80-952 Gdan´sk, Narutowicza 11/12, Poland c Institute of Physics and Biophysics, Warmia and Masuria University, M. Oczapowskiego 7, 10-719 Olsztyn, Poland

Received 30 July 2002; received in revised form 5 November 2002; accepted 6 November 2002

Abstract Excitation energy transport and trapping is studied for monomer – fluorescent dimer system of flavomononucleotide (FMN) in polyvinyl alcohol films (PVA). It is shown that the theory neglecting reverse energy transfer (RET) from dimers to monomers does not allow for the explanation of concentration quenching and concentration depolarization results presented herein. Much better agreement has been obtained using generalized energy transport theory in which fluorescent dimers are treated as imperfect traps for excitation energy. Such parameters like the dimer quantum yield and its emission anisotropy are estimated. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Excitation energy; Flavomononucleotide; Polyvinyl alcohol film

1. Introduction Flavins act as coenzymes and photoreceptors in many biological systems [1]. Flavin mononucleotide (FMN) seems to be especially important among these due to its role in the photoreception process. It has been shown previously that the properties of FMN in polyvinyl alcohol films (PVA) change dramatically at high dye concentrations [2– 4]. It has been found that FMN monomers at such high concentrations form aggregates which could be identified as dimers able to emit their own fluorescence in rigid polymer films [3,4]. These fluorescent dimers can act as imperfect traps for excitation energy, which means that they can transfer part of the excitation energy back to the set of monomers. The quantitative description of such forward and reverse transport is complicated, nevertheless, it has been elaborated theoretically [5 – 10] and confirmed experimentally for simpler model systems [11– 18].

$ Dedicated to Professor Alfons Kawski on the occasion of his 75th birthday. * Corresponding author. Tel.: +48-5855-29244; fax: +48-5834-13175. E-mail address: [email protected] (P. Bojarski).

The main difficulty in the quantitative description of reverse energy transport (RET) in the system studied is the lack of critical concentrations for energy transfer from dimers-to-monomers and between dimers. These quantities could not be obtained by the usually applied spectroscopic methods because of several reasons. First, it is very difficult to obtain pure dimer fluorescence spectrum [3,4]. Second, even if the dimers’ fluorescence spectrum could be known exactly, one should take into account that dimers can be excited both directly by light absorption and by receiving nonradiative energy from the monomers. Additionally, dimers can emit their own fluorescence and transfer energy back to the set of monomers. Therefore, the dimer quantum yield obtained by simple spectra separation is not, in principle, its ‘‘true’’ quantum yield. Finally, the spectra of monomers shift to the red with concentration due to inhomogeneous broadening of monomer energy levels [3,4]. This effect also limits the possibility of determining the dimer quantum yield using the spectroscopic method [3]. The aim of this paper is to describe quantitatively the behaviour of FMN concentrated PVA solutions. In particular, we propose a method to estimate the dimer quantum yield based on the best fit of concentration quenching and concentration depolarization of FMN in PVA to the theory

0304-4165/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0304-4165(02)00498-1

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of forward and reverse nonradiative energy transport recently elaborated. Also, dimer fluorescence anisotropy will be estimated based on concentration depolarization experiments performed under anti-Stokes excitation.

2. Theoretical basis By now, two models have been elaborated to describe forward and reverse energy transfer in donor – acceptor disordered systems. These are the hopping model (HM) and the self-consistent diagrammatic model (SCDM). HM is rather straightforward in applications, but it is also less accurate. This fact results from the simplifying assumption taken up during the derivation of emission anisotropy; that the excitation energy does not migrate back from energy acceptors (dimers) to those energy donors (monomers) which have been initially excited by the light absorption. As a result, emission anisotropy is somewhat lowered in this model compared to the respective expression obtained in the SCDM as well as to the experimental data [14]. Besides emission anisotropy, both models predict similar concentration and temporal courses of fluorescence observables. We will limit the theoretical part to considerations necessary for comparison with experimental data. Full theoretical description of HM can be found in Refs. [5– 9] and SCDM in Ref. [10]. The HM of forward and reverse energy transport predicts relatively simple expressions for luminescent observables. Relative monomer quantum yield and emission anisotropy are given by Refs. [5,9]: ð1Þ

rM ¼ ð1  af ðcÞÞð1  BÞ r0M

ð2Þ

where

! CD CM pffiffiffi DD þ DM ; C0 2C0

ð3Þ

aV¼

cDD cV ð4Þ

pffiffiffi p cMM ffiffiffi þ cMD ¼ c¼ p 2 2

N N NX þM X dpj X MM ¼ wMM p  w p  wMD k j jk kj kj pj dt k¼1 k¼1 k¼N þ1

þ

NX þM

wDM jk pk 

k¼N þ1

! CM CD pffiffiffi MM þ MD ; C0 2C0

a¼

cDD c ð5Þ

where c is the total reduced concentration for migration in the monomer ensemble and forward monomer-to-dimer energy transfer and cV is the total reduced concentration

pj ; s0M

1VjVN

ð7Þ

N N NX þM X dpj X ¼ wMD wDM wDD jk pk  kj pj þ jk pk dt k¼1 k¼1 k¼N þ1



NX þM

wDD kj pj 

pj ; s0D

N þ 1VjVN þ M

ð8Þ

The distance-dependent transfer rate from the j-th X molecule to the i-th Y molecule (X,Ya{M,D}) is denoted by wijXY (wiiXX = 0, wijXX = wjiXX). Its explicit form has been given by Fo¨rster [22]: 1 wxy ij ¼ s0x

ð1  aÞf ðcÞ ð1  aVÞf ðcVÞ 1  af ðcÞ 1  aVf ðcVÞ

pffiffiffi p cDD cV¼ pffiffiffi þ cDM ¼ 2 2

where erf (t) is the error function. For B = 0 (no reverse transfer) expressions (1) and (2) are identical to those obtained in HM of forward energy transport [19 – 21]. SCDM is much more complex and arduous in direct application, but it also gives very accurate results. Therefore, our analysis will be based mostly on this model. Let us consider a system of volume X in which energy can be transferred incoherently between N donors and M acceptors randomly distributed with number densities qD and qA, respectively. The probability that an excitation is on the jth molecule at time t, pj(t), for the fixed molecular configuration R obeys the following master equation [10]:

k¼N þ1

gM 1  f ðcÞ 1 ¼ g0M 1  af ðcÞ 1  B

B¼

for migration in the dimer ensemble and reverse dimer-tomonomer energy transfer, C0XY, {X,Ya{M,D}} denotes the critical concentration, and f(t), where ta{c,cV} is related to the error function: pffiffiffi f ðtÞ ¼ ptexpðt 2 Þ½1  erf ðtÞ ð6Þ



Rxy 0 R

6 ð9Þ

s0M and s0D are the lifetimes of the monomer and dimer molecules in the absence of the intermolecular energy transfer. The solution to Eqs. (7) and (8) can be expressed by the Green function [10,23]. The Green function G(r,rV,t) can be portioned into the diagonal part GSM(r,rV,t), which represents the density of the initial site survival probability (it can be measured in the fluorescence depolarization experiment), and the nondiagonal parts, GMM(r,rV,t) and GMD(r,rV,t), representing the probability densities of the excitation being found on a donor other than the initially excited one, and on an acceptor, respectively (they are related to the mean square displacement and to the fluorescence intensity decay function). Taking account of the reverse excitation energy transfer also demands that the Green functions, GSD(r,rV,t),

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GDD(r,rV,t) and GDM(r,rV,t), to be introduced. These additional Green functions describe the excitation energy dynamics in the dimer ensemble. Using the diagrammatic method, the above equations can be solved and expressions for luminescent observables can be found. In particular, the monomer emission anisotropy, rM/r0M, can be symbolically expressed as [10]: rM =r0M ¼ 1 

Rˆ MM  ˆ SM qM G

Rˆ MD Rˆ DM  ; ˆ DD R SM SD ˆ ˆ qM qD G G 1 ˆ SD qD G

e¼0

ð10Þ

where r0M is the so-called limiting donor emission anisotropy, recorded in a viscous medium (no rotational depolaˆ SM rization) and in the absence of any transfer processes. G SD ˆ and G represent the Fourier –Laplace transforms of the respective Green functions and Rˆ MM, Rˆ MD, Rˆ DM, Rˆ DD are the diagrammatic series which must be partly summed to yield appropriate approximations for the Green functions. For the relative donor quantum yield, the following expression is obtained [10]: gM ¼ g0M

1 s0M Rˆ MD =s0D qM 1þ ˆ SM ð1  Rˆ DD =qD G ˆ SD Þ G

ð11Þ

In the absence of RET, expressions (10) and (11) predict identical values of luminescent characteristics as in a simpler theory elaborated by Loring et al. [23] (LAF model). The detailed numerical procedure required for comparison of Eqs. (10) and (11) with experimental data has been outlined in Refs. [10,14,17]. To compare experimental values of gM/g0M and rM/r0M with those obtained from HM or SCDM, the critical concentrations must be known. Critical concentrations C0XY (X,Ya{M,D}) for monomer-to-monomer and for monomer-to-dimer energy transfer can be easily determined from the relation [22]: C0XY ¼ 4:23 1010 n2 ½g0X < j2 > IXY 1=2 ; X; YaðM; TÞ

ð12Þ

where n is the refractive index of the medium, g0X is the absolute quantum yield of the monomer, < j2> is the

203

averaged orientation factor and IXY is the spectral overlap given by: IXY ¼

Z

l

FX ðvÞeY ðvÞv4 dv

ð13Þ

0

Here, v is the wave number, eY is the decimal molar extinction coefficient of molecule Y and FX(v) is the spectral distribution of X molecule fluorescence normalized to unity over the frequency scale.

3. Monte Carlo simulation Since the results predicted by both models are generally not equivalent, as an invaluable and independent tool to compare both models and analyze experimental data, Monte Carlo simulation technique is used. In a simulation, N monomers of concentration CM and M dimers of concentration CD, are randomly distributed in a three-dimensional cube. The dynamics of the system considered is described by Eqs. (7) and (8). The effect of the finite size of the generated system is reduced by introducing periodic boundary conditions (the cube is surrounded by replicas of itself) with the minimum image convention (the molecule (monomer or dimer) interacts with another molecule or with its periodic image). The concentration course of the quantities of interest is obtained by rescaling critical radii for energy transfer and keeping the length of the cube edge equal to 1. The pseudo-random number generator (mixed congruential generator with the period of 232), which passed several statistical tests was also verified by checking the simulated statistical clusters concentration against the analytically expected value. The simulated configurations were sampled until the relative variance of the luminescent observables attained less then 0.1%. In our simulations, we used 2000 molecules. Each simulation run was repeated 10,000 times to obtain accurate averaging. For further details see Refs. [10,16].

4. Experimental FMN (riboflavin-SV-monophosphate sodium salt (C13 H20 N4 NaO9P 2H2O)) from Fluka AG and PVA from Loba-

Table 1 Selected spectroscopic parameters of FMN in PVA at several concentrations (kexc = 445 nm) CM (M) CD (M) r (experimental) g (experimental) (eM CM)/(eM CM + eD CD)

6.7 10 4 5 10 6 0.327 0.41 0.995

2.7 10 2 8 10 3 0.2 0.28 0.826

4.9 10 2 2.8 10 2 0.169 0.18 0.72

9.1 10 2 8.8 10 2 0.11 0.096 0.588

1.51 10 1 2.64 10 1 0.073 0.05 0.455

CM, CD denotes monomer and dimer molar concentrations, respectively; r and g are experimental emission anisotropy and fluorescence quantum yield, respectively; in the lowest row of the table, the fractions of monomers excited in the system are listed (eM(445 nm) = 11,700 1/(M cm), eD(445 nm) = 8000 1/ (M cm)).

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Table 2 The values of energy transfer parameters for FMN in PVA T (K)

kexc (nm)

n F 0.001

< j2>

g0M F 10%

r0M F 0.003

gD F 0.005

rD F 0.04

CMM (M) F 0 0.001

CMD (M) F 0 0.002

CDM (M) F 0 0.01

CDD 0 (M) F 0.01

293

445

1.654

0.476

0.4

0.34

0.02

0.17

0.051

0.031

0.09

0.50

Chemie, Vien-Fishamend, analytically pure, were used. FMN was dissolved in 10% aqueous solution of PVA at a temperature T = 333 K to obtain a homogeneous solution. The FMN molar concentration C in PVA films changed from 6.8 10 4 to 6.8 10 1 M. Samples were of such thicknesses d that the following relation (Eq. (14)) allowing for neglecting the reabsorption and reemission effects was fulfilled [24]: 2:3emax Cd < 0:1

ð14Þ

emax is the maximum value of the monomer extinction coefficient. To attain this PVA matrices containing FMN were prepared by drawing out glass plates from the FMN – PVA solution at appropriately adjusted speed and solution temperature. After this process, the samples were placed in a vacuum drier to allow slow water evaporation and polymerization process. For absorption measurements, a second series of samples was prepared with optical densities of an order of unity. This series helped to determine both dimer extinction coefficients and spectroscopic as well as energy transfer parameters. At all FMN concentrations we checked additionally the possible effect of polymer film interaction with the glass by measuring absorption spectra for both series of samples differing in optical densities. In the case of our system, we have found no significant change in spectra location and shape for respective samples. Tables 1 and 2 summarize some spectroscopic and energy transfer data of FMN in PVA. Quantum yields were determined based on absorption and fluorescence spectra measurements using previously determined quantum yield of FMN in water and in glycerol as standards. Fluorescence spectra were measured upon the front-side excitation and observation of the sample fluorescence using the apparatus described separately [25] and the results were corrected for the spectral sensitivity of the equipment as well as for the spatial anisotropy distribution of the polarized fluorescence. The temperature of each measurement was controlled with an accuracy of F 0.1 degree. Emission anisotropy was measured under similar conditions using two-channel single-photon counting apparatus described separately [12,26].

5. Results and discussion Fig. 1 shows the concentration dependence of FMN emission anisotropy in PVA upon the excitation, kexc= 445 nm, and at the observation, kobs = 530 nm. The observation at kobs = 530 nm corresponds approximately to the maxi-

mum of monomer fluorescence band (monomer band). Full circles correspond to experimental data of emission anisotropy. Curve 1 is obtained based on the energy transport theory, which treats dimers as perfect traps for the excitation energy and it does not take into account the process of RET (C0DM ! l). Both HM and LAF model, in this case, predict practically indistinguishable results represented by curve 1. As seen from the figure, experimental data cannot be described by this curve at cM>0.2. Curve 2, however, obtained from SCDM accounting for the RET, well describes experimental data presented over the whole concentration range. Curve 3 in this figure has been obtained based on the generalized HM accounting for RET. However, due to the simplification made in this theory while calculating emission anisotropy (discussed earlier in this work), curve 3 predicts somewhat lower values than those of SCDM and experimental data at highest FMN concentrations. It should be underlined that all the theoretical curves presented in this figure have been obtained for the same dimerization constant K = 11.6 M 1 determined from independent absorption measurements [3,4]. Also the same set of necessary parameters describing energy transport processes was used to obtain curves 1 –3 (cp. Table 2).1 Since the critical concentrations C0DM = 0.09 M and DD C0 = 0.5 M for dimer-to-monomer and dimer-to-dimer energy transfer, respectively, cannot be obtained directly from the spectral measurements, they are determined as best fit parameters of experimental data recorded in the monomer band to the general SCDM theory accounting for RET. Additionally, the results of Monte Carlo simulations (MC) of emission anisotropy are presented in this figure (triangles). They were performed for the same set of energy transfer parameters as listed in Table 2. It is seen that the results of MC are very close to those of SCDM (curve 2) and agree quite well with experimental data. As expected, they deviate strongly from the theoretical curve 1 neglecting the RET. They differ also to some extent from the HM of RET (curve 3), which is understandable keeping in mind the discussed simplification made in this model while calculating emission anisotropy. The MC results therefore confirm RET quantitatively in this system, as well as the advantage of SCDM over HM in the description of the system studied. Fig. 2 shows similar results of MC, but performed for different critical concentrations for the RET C0DM. Relatively small changes in this parameter (with other parameters fixed) results in a significant change of emission anisotropy

1 Curve 1 is based on simpler models neglecting RET. In these models, of course, critical concentrations CDM and CDD 0 0 do not appear.

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Fig. 1. Relative emission anisotropy versus monomer reduced concentration. Circles (.) denote experimental data measured under the excitation kexc = 445 nm and observation kobs = 530 nm at room temperature T = 296 K. Triangles (D) denote the results of Monte Carlo simulations. Curve 1 has been obtained based on HM/LAF model (no reverse energy transfer), whereas curves 2 and 3 stand for generalized SCDM (Eq. (10)) and HM (Eq. (2)), respectively.

course at high concentrations and disagreement with experimental data. Good agreement between experimental data and MC can be only obtained for C0DM = 0.09 M, a value

identical to that obtained based on the best fit of SCDM and experimental data (cp. Fig. 1). This is, in our opinion, a further strong argument for the correctness of our analysis.

Fig. 2. Monte Carlo simulations of emission anisotropy concentration course performed for several critical concentrations CDM for dimer-to-monomer energy 0 transfer. All other energy transfer parameters assumed in the simulations were the same as listed in Table 2.

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Fig. 3 shows the results of relative emission anisotropy versus FMN molar concentrations for several excitation wavelengths and the observation at kobs = 600 nm, where the dimer fluorescence is comparably strong or even stronger than that of monomers at their highest concentrations. As can be seen from the figure, the concentration depolarization of FMN in PVA is distinctly weaker under anti-Stokes excitation (kexc = 520 nm) than at the Stokes excitation (kexc = 445 nm). This is a result of the red edge effect [3,27]. Under strongly anti-Stokes excitation, kexc = 520 nm, energy transport processes are very weak. Additionally, at this wavelength, monomers absorb extremely weakly (and significantly weaker from dimers) and therefore at highest concentrations we can safely assume that we recorded practically only the fluorescence signal coming from dimers. Therefore, lowemission anisotropies observed at highest FMN concentrations are then due to partly depolarized fluorescence of dimers excited directly by light with kexc = 520 nm and not rather due to energy transfer processes. Additional confirmation for that can also be the untypical course of emission anisotropy recorded for that excitation compared to all other courses at intermediate concentrations, where depolarization appears due to energy migration. However, for the antiStokes excitation, kexc = 520 nm, it remains practically constant up to cM = 0.2, which evidences the lack of energy migration. From our measurements, we obtained for the dimer the average value rD c 0.17 F 0.04. The emission anisotropy value obtained for the dimer is much lower than that for the FMN monomer r0M c 0.34 F 0.003. It should be stressed that the dimer emission anisotropy value r = 0.17 F 0.04 concerns J1 band of that dimer (cp. Fig. 2B in Ref. [3]).

Fig. 4 presents the results of FMN monomer concentration quenching in PVA. As seen from the figure, experimental data denoted as open circles are distinctly above curve 1 neglecting the RET. However, curve 2 obtained based on SCDM is visibly closer to experimental results, though some difference is still present at highest concentrations. This is due to the contribution of fluorescent dimers to the total fluorescence recorded at such high concentrations. It should be mentioned that the HM accounting for RET in this case predicts the values of quantum yield very close to those of SCDM (curve not shown for the sake of clarity of the figure). It is also noteworthy that both fluorescence anisotropy and quantum yield concentration courses are described by the same set of physical parameters, which makes our analysis more reliable. From the difference between the experimental data and SCDM we estimated the quantum yield of the dimer as gD = 0.02 F 0.005. As expected, it is much lower than that of monomer at low FMN concentrations. Finally, it seems worthy to discuss frequently addressed question concerning the nature of excitation energy traps. Based on the concentration courses of absorption spectra (cp. Figs. 1 and 2 in Ref. [3]) these traps were identified as dimers formed in the ground state and able to emit their own fluorescence in a rigid PVA matrix in the red part of monomer fluorescence spectrum. Of course, the presence of higher-order aggregates cannot be excluded, but they do not manifest themselves spectrally in our system. Therefore, we decided to describe our system as approximately a twocomponent system. Another question corresponding to the latter problem concerns the possible presence of FMN excimers in our

Fig. 3. Relative emission anisotropy versus monomer reduced concentration measured under three different excitation wavelengths: kexc = 445 nm, kexc = 490 nm and kexc = 520 nm and observed at kobs = 600 nm (dimer fluorescence band).

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Fig. 4. Concentration quenching of FMN in PVA at T = 296 K. Excitation wavelength was kexc = 445 nm. Open circles (o) denote experimental data and full squares (n) correspond to the results of Monte Carlo simulations. Curve 1 has been obtained based on LAF/HM (no RET), whereas curve 2 represents SCDM (reverse transfer included).

system. This hypothesis can be, however, denied based on previous studies of FMN properties performed in liquid solvents. As is well known, the formation of excimers is a diffusion-controlled process and it would be much more pronounced in a liquid solvent compared to a rigid PVA matrix. However, earlier studies performed in water and glycerol – water solutions revealed that only nonfluorescent FMN aggregates were formed in these media [28,29]. Therefore, excimers as a source of additional traps for excitation energy can be neglected. Another possible quenching center could be the so-called statistical pair. The statistical pair is formed by any two molecules which are separated by a distance long enough to prevent a dimer formation but short enough to treat it as a system which can effectively collect excitation energy coming from outside the pair. The idea of a statistical pair as a quenching center has been formally used in several papers to remove the disagreement between the experimental data and a theoretical model. However, there is no convincing experimental or theoretical explanation of such a pair as a quenching center. Moreover, statistical pairs, contrary to dimers or other aggregates, have never been detected experimentally.

matrices. For the first time, a quantitative comparison was made for FMN in PVA between the experimental concentration courses of emission anisotropy as well as quantum yield with suitable theoretical models of energy transport. It was found that simpler models which do not account for the RET cannot describe experimental results at high FMN concentrations. The application of the generalized SCDM model leads, however, to a much-improved description of experimental data. This is due to the fact that FMN dimers are fluorescent in PVA matrix and must be treated as imperfect traps for excitation energy. Based on the analysis performed, it was possible to estimate some dimer fluorescence properties like its emission anisotropy and quantum yield. Further progress in the description of FMN concentrated rigid solutions is expected by making temperature studies of quantum yield, emission anisotropy and mean fluorescence lifetime. Among other things, this should enable us to evaluate the influence of orientational inhomogeneous broadening of energy levels on the characteristics measured, as well as to study the dimer role as perfect or imperfect trap depending on the temperature of a sample. With respect to this latter problem, we plan also to report energy transport study in axially oriented polymer films.

6. Conclusions and final remarks

Acknowledgements

In the current paper, we continued our studies on photophysical properties of FMN concentrated solutions in PVA

This paper has been partly made within the framework of the research project BW 5200-5-0310-2.

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