8412
J. Phys. Chem. 1995, 99, 8412-8419
Comparison of Calculated and Experimentally Resolved Rate Constants for Excitation Energy Transfer in C-Phycocyanin. 1. Monomers Martin P. Debreczeny? and Kenneth Sauer* Structural Biology Division, Lawrence Berkeley Laboratory and Department of Chemistry, University of California, Berkeley, California 94720
Jianhui Zhou$ and Donald A. Bryant Department of Molecular and Cell Biology and Center for Biomolecular Structure and Function, Pennsylvania State University, University Park, Pennsylvania 16802 Received: November 1.5, 1994; In Final Form: February 2, 1 9 9 9
Rate constants for excitation energy transfer in the light-harvesting protein, C-phycocyanin (PC), in the monomeric aggregation state, isolated from the cyanobacterium Synechococcus sp. PCC 7002, are calculated using Forster theory and compared with the results of time-resolved fluorescence measurements. In addition to the relative distances and orientations between chromophores, obtained from the crystal structure of PC, the Forster calculations require spectroscopic resolution of several properties of the chromophore types ($1 5 5 , aS4,p84) found in PC monomers, including absorption and fluorescence spectra, molar absorptivities, fluorescence quantum yields, and fluorescence lifetimes. The resolution of the first two properties, the chromophore absorption and fluorescence spectra, was described in a previous paper [Debreczeny et al. J. Phys. Chem. 1993, 97, 9852-98621. The assignments of the energy-transfer rate constants in PC monomers are confirmed here by time-resolved fluorescence anisotropy measurements of the PC monomers isolated from both the wild-type and a mutant strain (cpcBKZ55S)whose PC is missing the P I 5 5 chromophore. These fluorescence anisotropy measurements also allow one to extract the angles between the transition dipoles of the chromophores within the p l 5 5 - p 8 4 (34') and a 8 4 - p S 4 (27') chromophore pairs. The values of the inverse of the sum of the forward and back calculated Forster rate constants for energy transfer within the p l 5 5 - p 8 4 , ~ 8 ~ - / & 4 , and p 1 5 5 - a 8 4 chromophore pairs are 49, 158, and 890 ps, respectively, and are in excellent agreement with the experimentally measured values. It is concluded that the Forster model of resonant energy transfer in the weak coupling limit successfully describes the dominant energy-transfer processes in this protein in the monomeric state.
I. Introduction Light-harvesting complexes containing large arrays of chromophores that collect light and funnel the energy toward the photosynthetic reaction center are crucial to a photosynthetic organism's ability to grow under conditions of variable light intensity. Excitation energy transfer over an array of several hundred chromophores typically occurs in 100 to 200 ps with 90% or higher efficiency. Quantitative tests of the mechanisms by which light-harvesting systems perform with such high efficiency have been frustrated in the past for two main reasons: (i) a lack of structural information at the molecular level and (ii) the difficulty in separating the spectral properties of the individual chromophores in light-harvesting complexes. The phycobiliproteins are light-harvesting proteins found in cyanobacteria, red algae, and cryptophytes. In cyanobacteria, several different types of phycobiliproteins associate to form large (MW -1 x lo7), well-organized, light-harvesting complexes called phycobilisomes (PBS). The phycobiliproteinsare amenable to the study of energy transfer for just those reasons mentioned above that have complicated energy-transfer modeling in other light-harvesting proteins: (i) the detailed X-ray crystallographic structures of phycobiliproteins from several
' Current address: Chemistry Division, Argonne National Laboratory, Areonne. IL 60439. Current address: Department of Plant Biology, University of California, Berkeley, CA 94720. @Abstractpublished in Advance ACS Absrrucrs, April 15, 1995. I
0022-365419512099-84 12$09.00/0
organisms have now been and (ii) the phycobiliproteins contain few chromophores per protein subunit, making resolution of the individual chromophore properties more feasible than in many other light-harvesting proteins. Crystal structures of the phycobiliprotein C-phycocyanin (PC) isolated from three different organisms have been determined.',2 Each PC monomer contains three tetrapyrrole chromophores covalently attached to cysteine residues. Although the tetrapyrroles are chemically identical, interactions with the protein make each of the three chromophores spectroscopically unique. The goal of these studies is to understand the mechanism of energy transfer on the level of single-step transfer between chromophores. One way to approach this problem is by comparing PC isolated from a wild-type strain of cyanobacterium with PC isolated from mutant strains genetically engineered to be deficient in specific chr0mophores.4.~ In a previous paper," resolution of the absorption and fluorescencespectra of the chromophores in monomeric PC was described. In this paper, we describe how these spectra can be used, in conjunction with other properties of the chromophores and the crystal structure of PC, to calculate rate constants for energy transfer using the Forster model6 of resonant energy transfer in the weak coupling limit. These calculations are compared with experimentally determined rate constants, and this constitutes the most detailed test of Forster theory in a lightharvesting protein to date. Forster rate constants for energy transfer in PC were previously calculated by Sauer and Scheer.'~~However, the chro0 1995 American Chemical Society
Excitation Energy Transfer in C-Phycocyanin mophore spectra used in those calculations were estimated by deconvolution procedures that involved prior assumptions about their spectral band shapes. The chromophore excited-state lifetimes, also required for the Forster calculations, were assumed to be the same (1.5 ns) for all three chromophore types. The chromophore fluorescence quantum yields were estimated from the absorption strengths of the deconvoluted spectra determined for PC from a different organism, Mastigocladus laminosus. In addition to measuring the chromophore absorption and fluorescence line shapes more directly, we have made measurements of the fluorescence quantum yields, molar absorptivities, and excited-state lifetimes of the individual chromophores of PC from Synechococcus sp. PCC 7002. These improvements in the determination of the chromophore properties result in a much more accurate calculation of the Forster rate constants. 11. Methods and Materials Site-Selected Mutant Strains. Spectroscopic studies were performed on wild-type PC and on PC isolated from mutant strain PR6235 (cpcBK155S)of Synechococcus sp. PCC 7002 in which the cysteine at the 6155 position has been substituted with a ~ e r i n e .The ~ chromosomal copies of the cpcB and cpcA genes were deleted by interposon mutagenesis with a aph2 gene of Tn5 and trans-complemented with the biphasic shuttle vector pAQE19 which carries the wild-type cpcA gene and the mutant cpcB gene. PC monomers isolated from the mutant strain cpcB/ C155S and the wild-type strain are referred to in the rest of the paper as (aPC6*) and (aPCpPC), respectively. Growth Conditions and PC Isolation. The wild-type and mutant strains were grown as described by Gindt.9,'o The mutant strain PR6235 (cpcB/C155S)was grown in a medium that contained kanamycin (100 mg L-I) and ampicillin (2 mg L-I). PC was isolated from the wild-type and mutant strains and separated into subunits as previously described! Spectroscopy. Steady-state fluorescence spectra were measured on a Spex Fluorolog fluorimeter (Spex Industries, Edison, NJ). Samples were diluted to have a peak absorbance of less than 0.1 in a 1 cm cuvette. Samples were excited with an approximately 4 nm bandwidth of light, and the emission bandwidth was limited to (2 nm. Spectra were corrected for the wavelength dependence of the efficiencies of the monochromators and detector. Absolute fluorescence quantum yields, QF, were measured by comparison with reference dyes as described by Demas and Crosby for optically dilute solutions." The time-correlated single photon counting (TCSPC) instrument for measuring time-resolved fluorescence has been described in detail e l ~ e w h e r e . ' ~ ~The ' ~ instrument response function (IRF) was measured using a scattering solution in place of the sample. IRFs, measured either before or after each fluorescence decay measurement, were -55 ps (FWHM). At each emission wavelength, an approximately 10 ns fluorescence decay window containing 8192 channels was acquired until 10 000 counts had been accumulated in the peak channel. A polarizer set at 54.7" (magic angle detection) relative to the polarization of the laser was placed between the sample and the monochromator so that isotropic fluorescence decay was recorded. The fluorescence upconversion instrument for measuring time-resolved fluorescence with 1 ps time resolution is described elsewhere.I4*l5 Samples were flowed through the excitation beam to avoid accumulating products of photodestruction. The sample reservoir was chilled on ice. A total sample volume of -5 mL was used for each experiment. The path length of the flow cell was 1.0 mm. The optical density of the samples was
J. Phys. Chem., Vol. 99, No. 20, 1995 8413 typically 0.2 or less at the excitation wavelength to limit selfabsorption effects. IRFs were measured in the same way that the fluorescence upconversion signals were measured except that the monochromator was set to half the wavelength of the excitation source. 111. Results Calculation of Fdrster Rate Constants. The calculation of the Forster rate constants, kDA, can be broken up into four factors:
where C is a collection of constants, G is a geometric term dependent on the relative orientation and distance between the donor and acceptor chromophores, S is a collection of spectroscopic properties of the individual chromophores, and I is the integral of the overlap of the fluorescence spectrum of the donor with the absorbance spectrum of the acceptor. 1. The first term, C, is the most certain of the four parts of the calculation:
where NA is Avagodro's number and n is the index of refraction. Moog et a l l 6 have shown that the appropriate index of refraction to be used in eq 2 is that of the bulk solution (n = 1.33 for water at 20 "C). 2. The geometry factor, G, is calculated according to
where RDAis the distance between the centers of the transition dipole moments of the chromophores. KDA depends on the relative orientation of the unit vectors describing the direction of the chromophore transition dipole moments @D and PA for donor and acceptor, respectively) and their orientation relative to the unit vector separating their centers ( b ~as) shown , in eq 3b. A model of the arrangement of the chromophores in PC monomers, based on the crystal structure determined by Schirmer et al.,l is shown in Figure 1. The values of RDA,8, K, and G within PC monomers are shown in Table 1 as calculated from the crystal structures of PC isolated from Synechococcus sp. PCC 7002 (formerly Agmenellum quadruplicatum) at 2.5 8, resolution,' M. laminosus at 2.1 8, resolution,' and Fremyella diplosiphon at 1.66 8, resolution.2 8 refers to the angle between the donor and acceptor transition dipole moments. The transition dipole moments were estimated by fitting a line through the conjugated portions of the chromophores. A more refined calculation of the transition dipole moments was performed by Schamagl et U Z . ' ~ , ' ~ based on the crystal structure of PC isolated from M. laminosus. The effects of nearby amino acids were included in semiempirical calculations of the chromophore wave functions. The positions of carbon, nitrogen, and oxygen were fixed at the positions given by the crystal structure, but protonation states were estimated by energy minimization calculations. Several different arrangements of the protons (tautomers) were found to be within kT of the lowest energetic configuration. Transition dipoles were calculated by the monopole method. Values of RDA,8, K , and G, shown in s2
Debreczeny et al.
8414 J. Phys. Chem., Vol. 99, No. 20, 1995
TABLE 1: Distances, RDA,Relative Orientations, 8, Orientation Factors, K , and Geometry Terms, G, between the Transition Dipole Moments of Chromophores in Monomeric PC As Determined by X-ray Crystallography of PC Isolated from Three Different Species of Cyanobacterial.*
C-P hycocya nin Monomer
structural resolution chromophore R (A) pair 2.5
Syn. 7002b
Pls5-as4 48.0 34.2 50.5 as4-Ps4 /3]55-a84 47.7 (47.0) p155-p84 34.2 (33.7) 50.2 ~184-/384 (49.3) /3155-ax448.0 p155-/384 34.6 a84-px4 50.0 p155-/384
2.1
F. diplosiphond
1.66
G x 10-38 (cm-6)
62 47 16 66 (62) 49 (44.6) 18 (19) 69 55.9 15
0.43 0.77 1.72 0.58 (0.64) 0.84 (0.89) 1.73 (1.66) 0.242 0.684 1.706
0.15 3.70 1.78 0.29 (0.38) 4.40 (5.46) 1.87 (1.90) 0.048 2.74 1.86
a Transition dipole directions and centers were estimated by fitting a line through the conjugated portions of the chromophores.'%*The values in parentheses are the results of a semiempirical quantum mechanical calculation of the chromophore transition dipoles by the monopole method.l7-I9 Synechococcus sp. PCC 7002. Mastigocladus laminosus. Fremyella diplosiphon.
&
TABLE 2: Spectroscopic Properties of the Chromophores in Monomeric PC" chromophore
P84
15650 cm-'
M. laminosusC
/K/
A
(1)O(deg)
organism
pi55
aS4 p84
15850 cm-l
0
E x 10-8 (cm2mol-])
t (ns)
tg, (ns)
&C
(ns)
0.25 f 0.02 1.12 f 0.05 0.93 1.0.17 3.7 1. 0.7 3.65 0.23 f 0.02 1.15 & 0.05 1.50 fO.O1 6.6 f 0.6 4.43 0.19 f 0.02 0.701 i 0.03 1.45 f O . O 1 7.3 f 0.8 5.86
a CP is the fluorescence quantum yield, E is the absorptivity per mole of chromophore, t is the observed fluorescence lifetime, and t0 is the intrinsic fluorescence lifetime. The values of CP, E , and t for the a 8 4 chromophore were measured directly using isolated aK. The uncertainties are based on repetition of the measurements using different samples. The values of CP and E for the /& and chromophores were calculated by multiplying the relative values given in Tables 1 and 3 of ref 4 by the absolute values shown in this table for the aS4 chromophore. The values o f t for the P 8 4 and , 4 5 5 chromophores were calculated from the experimentally measured lifetimes of am,(aKpK), and (apcp*) (see main text for more details). T & , ~ is t divided by CP. t&cvalues for the three chromophore types were calculated directly from the resolved absorption and fluorescence spectra (eq 7, see ref 4 for spectra).
16250 cm-'
(4)
where E is the maximum visible molar absorptivity (cm2mol-'), zo is the intrinsic fluorescence lifetime (s), and CP is the fluorescence quantum yield of the chromophores. 't represents the observed fluorescence lifetime of the chromophore in the absence of energy transfer. The quantities used in the calculation of S are shown in Table 2. The molar absorptivity of the a 8 4 chromophore was determined by comparing the absorbance of aptunder denaturing (8 M urea, pH 2) and nondenaturing (5 mh4 (Na) phosphate, pH 7) conditions. The molar absorptivity of apc under denaturing conditions, as determined by Glazer and Fangz0is 0.332 x IO5 M-' cm-' at 662.5 nm. The
maximum absorbances of the p84 and p i 5 5 chromophores relative to the ag4chromophore (given in Table 1 of ref 4) were scaled by the absorptivity of the a84chromophore to produce the values in Table 2. The fluorescence quantum yield of the a84 chromophore was measured by comparing the integrated emission spectrum of apcin 5 mM (Na) phosphate, pH 7, excited at 560 nm, to that of cresyl violet in methanol. Magde et aL2' report a fluorescence quantum yield of 0.545 for cresyl violet perchlorate (Exciton Inc., Dayton, OH) in methanol at 22 "C in equilibrium with air. The quantum yield of apcwas corrected for the difference in index of refraction between water and methanol, but this correction was smaller than the uncertainty of our reported quantum yield. The fluorescence quantum yields of the p84 and /3155 chromophores relative to the aS4 chromophore (given in Table 3 of ref 4) were scaled by the absolute quantum yield of the as4chromophore to generate the values in Table 2. The isotropic fluorescence lifetimes of apc,(aPCPPC), and (aPC/3*) were measured by the TCSPC technique (see Figure 2) for the purpose of resolving the individual z values of the three chromophore types in PC monomers. Immediately
0
(99)
0002
OOOt
2
2
2 a
3
0009
0008
00001
SIPS 5661 ‘02 ’ON ‘66 ‘PA “ W a W ’skzld T
m
8416 J. Phys. Chem., Vol. 99, No. 20, 1995 cpcB/C155S mutant
,
0.4
Debreczeny et al.
/
O
0.3 0 x.
e
L
.-In
I a,
2
0.2
0
a,
.
b
U.
/
\
wild-type
\
0.1'
IRF, 5 ps FWHM
0.0. 0
400 600 Oelay Time (ps)
200
800
Figure 3. Fluorescence anisotropy decay of (aPCpPC) and (a"B*) measured by the fluorescence upconversion technique at room temperature. Excitation is at 592 nm, and emission is observed at 659 nm. The instrument response function (IRF) is also shown for comparison. TABLE 3: Overlap Integrals (I x 10l8 cm4, see eq 8) for the Chromophores in Monomeric PC based on the Room Temperature Absorption and Fluorescence Spectra Resolved in Ref 4 acceptors donors BlSS a84 884 pi55
a84 Pa4
5.60 2.16 1.25
7.81 4.50 3.47
9.97 7.49 6.96
spectrum of the acceptor (AA).
The resolution of the absorption and fluorescence spectra of the chromophores, used in eqs 7 and 8, was described in ref 4. The absorption spectra were measured at 1 nm intervals and for eq 8 were normalized to peak at 1. The chromophore fluorescence spectra were measured at 5 nm intervals and linearly interpolated to a 1 nm interval. The overlap integrals in monomeric PC at room temperature are shown in Table 3. The results of combining the four terms in the Forster calculation are shown in Table 4. The calculations were performed using geometry factors derived from the crystal structures of PCs isolated from three different species of cyanobacteria. Calculations using the refined transition dipole moments of Scharnagl et al."-I9 for PC isolated from M. laminosus are given in Table 4 in parentheses. All chromophore properties used in the calculations, other than the geometry
factors, were as determined for PC isolated from Synechococcus sp. PCC 7002. Both calculated and experimentally determined intrinsic fluorescence lifetimes were used to calculate the rate constants in PC isolated from Synechococcus sp. PCC 7002. Only the experimentally determined intrinsic fluorescence lifetimes were used in calculating the rate constants in PCs isolated from other organisms. Ratios of back to forward rate constants were calculated using eq 5c and are the same in the third and fourth rows of Table 4 as in the first row because the ratio of the rate constants is independent of the specific geometry of the chromophore interaction. Experimentally Determined Rate Constants. Experimentally determined rate constants for energy transfer in monomeric PC are shown below the theoretical predictions in Table 4. The first row of experimental rate constants was determined using the TCSPC technique by modeling the decay of isotropic fluorescence in /?Eand (aEp*), as described in ref 4. To check our results by a second method, we used fluorescence upconversion to monitor the anisotropic fluorescence decay of (apcppc)and (apcp*). Typical decays are shown in Figure 3, for which the samples were excited at 592 nm and emission was observed at 659 nm. Note that the anisotropy of (aE/?*) decays more slowly and to a lesser extent than (aPCpE). Qualitatively, it is clear from Figure 3 that removing the /?I55 chromophore from the monomer has decreased the number of routes by which the initial excitation can be depolarized. The anisotropy decays were quantitatively fitted using the model described in the Appendix. The time-resolved fluorescence anisotropy is dependent on the relative absorption and fluorescence of the chromophores, the relative spatial orientations of the chromophores, and the rate constants for energy transfer between the chromophores. In the fits, the relative absorption and fluorescence of the chromophores were set at the values determined in ref 4 (Figures 1 and 9). There is insufficient information to simultaneously extract the forward and back rate constants between chromophore pairs, so the ratios of the forward to back rate constants were fixed at the values determined by the Forster calculations and the sums of the forward and back rate constants were allowed to vary during the fits. The relative spatial orientations of the chromophores were initially set to the values predicted by the crystal structure (as determined by Schirmer ef al. in Synechococcus sp. PCC 7002). However, the fits to the anisotropy decays were poor unless this orientation was varied in addition to the summed forward and back rate constants. For (apc/?*) a two-chromophore ( a 8 4 and P s ~model ) was used. Four decays excited at 592 nm and emitting at 641, 650, 659, and 673 nm were measured. The decays were both individually and simultaneously (globally) fit, with similar results. The inverse of the summed forward and back rate constants was fit to 200 f 70 ps, in agreement with the TCSPC result of 149 f 2 ps. The angle between the transition dipole moments of the as4and p84 chromophores was fit to 27 & 1So. This is somewhat different from the 16' angle predicted from the crystal structure by Schirmer et al. Thus, although the experimental anisotropy of (aEp*>decays only to a small extent (residual anisotropy of 0.33 in Figure 3) compared to that of (apcpE),the crystal structure leads to a prediction of even less decay (residual anisotropy of 0.38). The difference in the predicted and observed chromophore orientations might reflect a difference between the structure of crystalline PC in the hexameric state and solvated PC in the monomeric state. The residual anisotropy would also be lowered if the absorption and emission transition dipoles of the individual chromophores were
J. Phys. Chem., Vol. 99, No. 20, 1995 8417
Excitation Energy Transfer in C-Phycocyanin
TABLE 4: Energy-Transfer Rate Constants for Donor-Acceptor Pairs (a-b) in C-Phycocyanin Monomers from Forster Calculations and from Time-Resolved Fluorescence Experiments. kab refers to the Rate Constant for Energy Transfer from Chromophore u to Chromophore b
organism
noteslref
Syn. 7002" Syn. 7002" M. 1amin.b
F. diplos.'
g
PI5 5 - a ~ 890 f 150 815 460 (350) 2,800
Syn. 7002" Syn 7002"
TCSPC' 4 upconvl
k
Syn. 7002" M. l a m k b F. diplos.' P . luridumd
8 8 2 27
370 200 25,000
> 500
P155-pa4
P i 5 5- a 8 4
a 8 4 - P ~
Forster Calculations 49 5 8 158 i 12 46 111 41 150 (33) (148) 66 151 Experimental Results 52 f 10 149 f 2 45 f 15 200 i 70 Previous Forster Calculations 24 41 20 39 770 530 1.7 10.0
PI55-PS.4
a84-Ps4
0.15 f 0.03 0.22 h
0.10 i 0.02 0.12 h
0.65 i 0.1 0.57 h
h
h
h
k k
'0.2 k
'0.5 k
0.24 1 m 0.13
0.22 1 m 0.03
0.76 1 m 0.12
a Synechococcus sp. PCC 7002 (formerly Agmenellum quadruplicatum). Mastigocladus laminosus. Fremyella diplosiphon. Phormidium luridum. These Forster calculations were performed using intrinsic fluorescence lifetimes that were calculated directly from the resolved absorption and fluorescence spectra (eq 7). In all other Forster calculations summarized in this table, we used the experimentally determined intrinsic fluorescence lifetimes (see text and Table 2). /Transition dipoles calculated by Schirmer et a1.I Transition dipoles calculated by Scharnagl et a1.17.18 Values are the same as for Syn. 7002, since the ratio of back to forward energy transfer is independent of the distance and orientation of the chromophore pair. Measured by the time-correlated single photon counting technique. 1 Measured by the fluorescence upconversion technique. Values were not resolved experimentally. The ratio of forward to back energy-transfer rate constants are the same in this row as in the row above because the properties of PC in Synechococcus sp. PCC 1002 and M. laminosus were not differentiated by the authors (PC from M. laminosus was used to estimate the chromophore properties). Forward and back energy-transfer rate constants were not differentiated in these calculations.
e
nonparallel. However, the fact that the anisotropy decay of (aK@*) in Figure 3 starts near 0.4 indicates that they are nearly parallel. Modeling the (apcPK)fluorescence anisotropy decay requires a three-chromophore model. The rate constants and orientations determined in (apCP*) were used as fixed parameters in this model. Coupling between the p l 5 5 and a 8 4 chromophores was initially neglected. With these simplifications, there are again only two variable parameters: the summed forward and back rate constants for energy transfer between the p i 5 5 and chromophores and the angle between their transition dipole moments. The sum of the forward and back rate constants from the fit was 45 f 15 ps, again in agreement with the TCSPC results of 52 f 8 ps. The angle between the p l 5 ~and transition dipole moments extracted from the fit was 34 f 5". This is again different from the angle of 47" calculated from the crystal structure.' Alternatively, when fitting the (apcpPc)fluorescence anisotropy decays, the summed forward and back rate constants for energy transfer between the a84-/384 and p155-p84 pairs were fixed at the values determined in the TCSPC experiments, and the summed rate constant for energy transfer between the p,,,a 8 4 pair was allowed to vary. The ratios of back to forward energy transfer were fixed as determined by the Forster calculations, and the relative orientations of the chromophores were fixed as determined by the crystal structure. The sum of the rate constants for energy transfer between the p 1 5 5 - a ~ 4 pair fit to zero within the estimated uncertainty, with a maximum value of 2 ns-' at the limit of the uncertainty.
IV. Discussion The first row in Table 4 shows the results of our calculations of the Forster rate constants for energy transfer in monomeric PC isolated from Synechococcus sp. PCC 7002. These calculated rate constants show excellent agreement with our experimentally determined rate constants also listed in Table 4 (see
also Figure 1) and with those previously measured (see Table 5 in ref 4). The estimated uncertainties in the calculated Forster rate constants are based on the uncertainties in the measurements of the quantum yields of fluorescence, the molar absorptivities, and the observed fluorescence lifetimes of the individual chromophores in monomeric PC. Alternatively, the intrinsic fluorescence lifetimes of the chromophores were calculated directly from their absorption and fluorescence spectra. The rate constants predicted using these calculated intrinsic fluorescence lifetimes (second row in Table 4)show slightly worse agreement with the experimental rate constants than do the rate constants predicted from the experimentally measured intrinsic fluorescence lifetimes. Both methods have inherent difficulties. The experimental measurement of the observed fluorescence lifetimes of the chromophores suffers from the fact that apc, containing a single chromophore, shows a multiexponential fluorescence decay from its excited ~ t a t e . * ~ -The * ~ decay is dominated by a single component that accounts for about 90% of the observed intensity; nevertheless, assigning the lifetimes of the chromophores to single values is an approximation. On the other hand, direct calculation of the intrinsic fluorescence lifetimes from eq 7 relies on the assumption that the ground and excited electronic states of the chromophores have the same vibrational structure. This too is an approximation, although for the rigidly held chromophores of PC it seems reasonable. Another source of error in our calculations, which is not accounted for in the reported uncertainties, is in the assignment of the transition dipoles of the chromophores used to calculate the geometry factor, G (eq 3). There is a potential for error both due to the finite resolution of the crystal structure and in calculating the transition dipole moments from this structure. The relative chromophore transition dipole orientations reported for PCs isolated from different organisms are shown in Table 1. The rate constants predicted using these different transition dipoles are shown in Table 4 (all chromophore properties used in the calculation, other than the transition dipoles, are as
Debreczeny et al.
8418 J. Phys. Chem., Vol. 99, No. 20, 1995
observed in Synechococcus sp. PCC 7002). Of course, it is quite likely that there are real differences between the orientations of the chromophores in PCs isolated from different organisms, but the differences between the calculated rates in PCs from the three different organisms can be taken as an indication of the upper limit of the uncertainty in the rate constant calculations due to structural uncertainty. The transition dipole moments were estimated from the crystal structure by fitting a line through the conjugated portions of the chromophores.',* Quantum mechanical calculations of the transition dipoles were also performed on the chromophores found in PC isolated from M. laminos~s.'~-'~ The geometry of the transition dipoles and the Forster rate constants resulting from these two different methods of calculating the dipoles are compared in Tables 1 and 4, respectively. The differences between the Forster rate constants in PC from M. laminosus resulting from these two different methods of calculating the transition dipoles are smaller than the uncertainties in the rate constant calculations in PC from Synechococcus sp. PCC 7002.
V. Conclusions On the basis of the results described here, the excitation energy transfer processes occurring in monomeric PC are well described by Forster theory. Of the three possible pairs between which energy transfer could take place, only the p155-pS4 and a84-Pg4 pairs undergo excitation energy transfer that is rapid compared to the net radiative decay (1-2 ns) of the chromophores. The inverse of the sums of the forward and back rate constants for energy transfer within the p155-p84 and as4p s 4 pairs are 50 and 150 ps, respectively, as measured experimentally and as calculated using Forster theory (see Table 4). Interestingly, the p155-as4 and as4-PE4 chromophore pairs are separated by approximately the same distance (50 A), yet no energy transfer is experimentally observed within the PISaS4pair. This is again confirmed by the Forster calculations which show that the weak coupling within the /h5-aS4pair is due to the unfavorable orientation of the chromophore transition dipole moments for resonant energy transfer. Previous calculations of the rate constants for energy transfer in PC monomers are shown at the bottom of Table 4. The calculations of Duerring et al.*, intended as estimates, were based on the formula
(9) Forward and back rate constants for energy transfer were not differentiated. KDA and RDAwere taken from the crystal structure of PC isolated from F. diplosiphon.* ZD and RO,DAwere taken as 2.2 ns and 50 A, respectively, on the basis of the work of Grabowski and Gantt.*6 These parameters are in reasonable agreement with our results (we find ZD = 0.93- 1.5 ns and RO,DA = 44-63 A). Nevertheless, the rate constants calculated by Duerring et d 2are dramatically different from our calculations and from the experimentally measured rate constants. The essential difference between the calculations of Duerring et al. and the present calculations is that Duerring et al. ignored the spectroscopic differences (molar absorptivities, fluorescence quantum yields, radiative lifetimes, and shapes of absorption and fluorescence spectra) between the three chromophore types in PC. The resulting disparity between the calculated and experimentally measured rate constants provides convincing evidence that the unique spectroscopic properties of each chromophore type cannot be ignored.
Forster calculations where attempts were made to take into account the spectral differences of the three chromophore types in PC have been reported by Grabowski and BjOmz7 and by Sauer and Scheer.8 In both these cases, Gaussian deconvolution procedures were used to approximate the resolved spectroscopic properties of the three chromophore types. A single radiative lifetime was used for all three chromophore types. In the case of Grabowski and Bjom, the same fluorescence quantum yield (0.52) was used for the three chromophore types. Sauer and Scheer assumed that the fluorescence quantum yield is proportional to absorption strength and scaled these values relative to the experimentally measured quantum yield of the apcsubunit isolated from M. laminosus (0.72). In the present work, the improved agreement between the calculated and experimental rate constants for energy transfer in monomeric PC over previous work is due to an improvement in the resolution of the properties of the individual chromophores. This includes a more direct resolution of the absorption and fluorescence spectra, which are used to calculate the overlap integrals (eq 8), as well as new measurements of the chromophore fluorescence quantum yields, molar absorptivities, and fluorescence lifetimes. Finally, the question of the relevance of the energy-transfer processes in monomeric PC to the functioning of PC in the whole PBS should be considered. Since excitation introduced into the rods of the PBS has been observed to reach the PBS core within 200 P S , *it~ is unlikely that energy transfer between the and as4 chromophores, or even the a 8 4 and p84 chromophores within a single monomer of PC, are important paths for energy transfer within the whole PBS. It is more likely that transfer from P I 5 5 to p84 chromophores within a single monomer of PC plays a role in PBS kinetics, especially as the probability of back transfer is relatively small. We will show in the following paper15 that the coupling between the p 1 5 5 and p84 chromophores within a single monomer remains an important kinetic process in PC trimers, while energy transfer between aE4 and p84 chromophores on the same monomer becomes insignificant compared to coupling of these chromophores between adjacent monomers. In any case, confirmation of Forster theory in PC monomers provides the groundwork for similar studies in higher aggregates of PC and in the whole PBS. Appendix: Time-Resolved Fluorescence Anisotropy The experimentally measured fluorescence anisotropy, I, is calculated from the fluorescence signals collected with parallel (Ipara) and perpendicular (Iperp)polarizations relative to the excitation beam, according to
where ilex and ,Iemare the wavelength of the excitation laser and the wavelength at which emission is observed, respectively. The parallel and perpendicular fluorescence intensities are modeled by considering the fate of the excitation energy when it is initially placed on each different chromophore in the system. This analysis assumes that excitation densities are limited to one photon absorption per light-harvesting complex. The relative probability of a particular chromophore being excited initially depends on its relative absorption at the excitation wavelength. The contribution of a particular chromophore to the observed fluorescence depends on its excited-state population as a function of time as well as its relative emission intensity at the observation wavelength. The relative contribution of a particular chromophore to the parallel and perpendicular fluo-
J. Phys. Chem., Vol. 99, No. 20, 1995 8419
Excitation Energy Transfer in C-Phycocyanin rescence intensities also depends on which chromophore in the system was initially excited. Transfer of excitation energy from an initially excited chromophore to a spectrally identical but orientationally different chromophore leads to a decrease in the observed parallel polarized emission intensity by a factor of (2y2 1)/3 and an increase in the perpendicular polarized emission intensity by a factor of (2 - y2), where y is the cosine of the angle between the transition dipole moments of the two chromophores. Combining these dependences to describe the fluorescence anisotropy of a model containing two nonidentical chromophores, one has
+
Ipara(tJex,Aem)
+
+ l)bl,O(tlfb(Aem)} + + l)ai),l(tlfa(Aem) + 3b0,1(t)fb(Aem)} (A2a)
‘b(&x){(2y2
=
ra(~e,){al,o(t)f,(il,,> Eb(Aex){(2
+ ( 2 - r2)bl,0(t)fb(nem)} +
- y2>ao,l(t)fa(nem>
+ bO,l(flfb(Aem)}
(A2b)
ex is the relative absorbance of chromophore x, while fx is the relative emission intensity of chromophore x . The subscripts
on the excited-state population terms denote which chromophore the excitation started on, with (1,O) indicating that the excitation started on chromophore a and (0,l) indicating that the excitation started on chromophore b. Substituting the chromophore population equations (see Appendix of ref 4) into the above equations (A2), one finds that
Z,,
= {3A,
+ (2y2+ 1)A2+ [3A, - (2y2
Ipev = {A,
+ 1)A2]e-f(k‘b+k~)}e-fkd (A3a)
+ (2 - Y 2 Y 2 + [A, - (2 - y2)A2]e-‘(kab+kba)}e-fkd (A3b)
where
A, =
‘afakba ‘ab
+ +
1 r(t) = -{(3y2 1 ) 3(1 - y2)e-2‘k} (A4c) 10 as has previously been shown e l ~ e w h e r e . ’ ~ , ~ ~ , ~ ‘ Acknowledgment. This work was supported by the Director, Office of Energy Research, Division of Energy Biosciences, of the U.S. Department of Energy under Contract No. DE-AC0376SF-00098 (M.P.D. and K.S.)and by U.S. Public Health Service Grant GM-31625 (D.A.B.).
=
‘ a ( ~ e ~ ) { ~ ~ l , O ( ~ ) f a ( (~2e ym2)
Ipq(tr&xJem)
and the anisotropy can be simply expressed as:
-k
‘db‘ab
+ kba
A, =
‘afa‘ab ‘ab
A, =
+ ‘db‘ba + kba ‘afa‘ab ‘ab
+ ‘bfb‘ba + ‘ba
(A3c)
Substituting eqs A3a,b into eq A l , we can see that the residual anisotropy of a model system containing two nonidentical chromophores is
r(=) =
2A,
+
(3y2 - 1)A2 5A, 5A,
+
(-434
Identical results are obtained if the method of Cross et is used to calculate the fluorescence anisotropy of a two-chromophore system. If the two chromophores have identical properties, eqs A3a-c simplify to
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