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Fo¨ rster Excitation Energy Transfer in Peridinin-Chlorophyll-a-Protein
Foske J. Kleima,* Eckhard Hofmann,
†
Bas Gobets,* Ivo H. M. van Stokkum,* Rienk van Grondelle,*
Kay Diederichs,
†
and Herbert van Amerongen*
*Faculty of Sciences, Division of Physics and Astronomy and Institute for Condensed Matter Physics and Spectroscopy, Vrije Universiteit,
1081 HV Amsterdam, the Netherlands, and
†
Fakulta¨t fu¨ r Biologie, Universita¨ t Konstanz, D-78457 Konstanz, Germany
ABSTRACT Time-resolved fluorescence anisotropy spectroscopy has been used to study the chlorophyll a(Chl a)toChla
excitation energy transfer in the water-soluble peridinin–chlorophyll a–protein (PCP) of the dinoflagellate Amphidinium
carterae. Monomeric PCP binds eight peridinins and two Chl a. The trimeric structure of PCP, resolved at 2 Å (Hofmann et
al., 1996, Science. 272:1788–1791), allows accurate calculations of energy transfer times by use of the Fo¨ rster equation. The
anisotropy decay time constants of 6.8 60.8 ps (
t
1
) and 350 615 ps (
t
2
) are respectively assigned to intra- and
intermonomeric excitation equilibration times. Using the ratio
t
1
/
t
2
and the amplitude of the anisotropy, the best fit of the
experimental data is achieved when the Q
y
transition dipole moment is rotated by 2–7° with respect to the yaxis in the plane
of the Chl amolecule. In contrast to the conclusion of Moog et al. (1984, Biochemistry. 23:1564–1571) that the refractive index
(n) in the Fo¨rster equation should be equal to that of the solvent, ncan be estimated to be 1.6 60.1, which is larger than that
of the solvent (water). Based on our observations we predict that the relatively slow intermonomeric energy transfer in vivo
is overruled by faster energy transfer from a PCP monomer to, e.g., the light-harvesting a/ccomplex.
INTRODUCTION
The dinoflagellate Amphidinium carterae contains a water-
soluble peridinin–chlorophyll a–protein (PCP) that acts as
an accessory photosynthetic light-harvesting pigment-pro-
tein complex. The complex transfers its excitation energy to
photosystem II (PSII) (Mimuro et al., 1990). However, it is
not known whether this transfer is directly to the PSII
antenna complex (Knoetzel and Rensing, 1990) or via the
membrane-bound light-harvesting complex (LHCa/c) (Hof-
mann et al., 1996). The main light-absorbing pigment of
PCP is peridinin, which absorbs in the 470–550-nm region.
Besides peridinin the complex binds chlorophyll a(Chl a).
The pigments are bound to a 30.2-kDa protein and are
organized into two clusters of pigments, each consisting of
four peridinins and one Chl a(see, e.g., Carbonera and
Giacometti, 1995). Singlet energy transfer from peridinin to
Chl aoccurs with an efficiency close to 100% (Song et al.,
1976; Koka and Song, 1977) on a time scale of a few
picoseconds (Bautista et al., 1999; Akimoto et al., 1996).
Recently, the crystal structure of PCP was resolved at a
resolution of 2.0 Å (Hofmann et al., 1996), revealing a
trimeric organization of the complex. The protein mainly
has an
a
-helical structure and forms a cavity in which the
two pigment clusters are located (Hofmann et al., 1996).
The distance between the centers of the two Chl ain one
monomer is 17.4 Å, whereas the distance between two Chl
abound to different monomers ranges from 40 to 54 Å
(Hofmann et al., 1996). All peridinins are organized in pairs
with a closest distance to each other of 4 Å, and they are in
van der Waals contact with the Chl a. The resolution is high
enough to distinguish the xand yaxes of the Chl amole-
cules, allowing a definition of the orientation of the Q
y
transition dipole moment within the molecular frame of Chl
ain PCP. Therefore, PCP forms an excellent system for the
study of the Chl ato Chl aexcitation energy transfer in a
relatively simple pigment-protein complex and to test
whether it can be modeled using the Fo¨rster equation (Fo¨r-
ster, 1965).
A detailed test of the Fo¨rster equation was conducted
before by Debreczeny et al. (1995a,b) on another pigment-
protein complex with a known crystal structure (Schirmer et
al., 1987; Duerring et al., 1991), namely monomeric and
trimeric C-phycocyanin (CPC) from Synechococcus sp. The
pigments responsible for light harvesting in this complex
are open-chain tetrapyrrole chromophores (also called phy-
cocyanobilins). The three pigments bound to each monomer
are relatively far apart; however, in the trimer two pigments
bound to different monomers are relatively close. The en-
ergy transfer processes in the monomeric and trimeric com-
plexes were studied using time-resolved polarized fluores-
cence experiments by Gillbro et al. (1993) and Debreczeny
et al. (1995a,b). It was concluded by Debreczeny et al.
(1995a,b, 1993) that the equilibration rates are in good
correspondence with those that can be calculated using the
Fo¨rster equation, with the refractive index (which is an
important parameter in this equation) being that of the
solvent, in this case water (n51.33). It was argued before
by Moog et al. (1984) that when the Fo¨rster equation is
applied to protein-chromophore complexes, the refractive
index of the solvent should be used.
In the present study we focus on the Chl ato Chl a
excitation energy transfer in PCP, using time-resolved flu-
orescence anisotropy spectroscopy. We show that the ex-
Received for publication 3 June 1999 and in final form 2 September 1999.
Address reprint requests to Dr. Foske J. Kleima, Division of Physics and
Astronomy, Faculty of Sciences, Vrije Universiteit, De Boelelaan 1081,
1081 HV Amsterdam, the Netherlands. Tel.: 31-20-444-7941; Fax: 31-20-
444-7999; E-mail: foske@nat.vu.nl.
© 2000 by the Biophysical Society
0006-3495/00/01/344/10 $2.00
344 Biophysical Journal Volume 78 January 2000 344–353
perimental equilibration rates and the rates calculated using
the Fo¨rster equation are in reasonable agreement when the
Chl aQ
y
transition dipole moments are oriented along the
molecular yaxis. However, we find a better match when
these dipole moments are rotated by 2–7°. In contrast to the
conclusion by Moog et al. (1984), in the case of PCP the
refractive index in the Fo¨rster equation is larger than the
refractive index of the solvent, which is water, and it is
estimated to be 1.60 60.1.
MATERIALS AND METHODS
Sample preparation
PCP was purified according to the method described by Hofmann et al.
(1996). Measurements were performed in a buffer containing 25 mM
Tris-HCl (pH 7.5), 3 mM NaN
3
, and 2 mM KCl.
Absorption and steady-state fluorescence
emission spectroscopy
The absorption spectra were recorded on a Cary 219 spectrophotometer,
using an optical bandwidth of 1 nm. Steady-state fluorescence emission
spectra were recorded using a CCD camera (Chromex Chromcam 1) via a
1
⁄
2
m spectrograph (Chromex 500IS). Excitation light was provided by a
tungsten-halogen lamp via a band-pass filter at 475 nm with a full width at
half-maximum (FWHM) of 15 nm. The fluorescence emission spectra were
corrected for the wavelength sensitivity of the detection system.
Time-resolved fluorescence anisotropy
The optical density of the sample was 0.2/cm at the excitation wavelength
(660 nm) and 0.6/cm in the absorbance maximum at 670 nm. The sample
was kept at room temperature in a spinning cell (light path of 0.22 cm,
diameter 10 cm, frequency 15 Hz) refreshing the sample every few shots.
The spinning cell was placed at an angle of 45° with respect to the
excitation light. Comparison of the OD spectrum of the sample before and
after the experiment showed that less than 10% of the absorption was lost
after an experiment with a duration of several hours. The spectrum essen-
tially did not change. Two independent series of experiments were performed.
Pulses of 150–200 fs at 660 nm with a FWHM of 7 nm were generated
at a 100-kHz repetition rate, using a Ti:sapphire based oscillator (Coherent
MIRA), a regenerative amplifier (Coherent REGA), and a double-pass
optical parametric amplifier (OPA-9400; Coherent). The intensity was
adjusted so that less than 1 photon/20 trimeric complexes was absorbed per
laser shot. The polarization of the excitation light was adjusted with a
Soleil Babinet compensator.
The fluorescence was detected at a right angle with respect to the
excitation beam through a sheet polarizer, using a Hamamatsu C5680
synchroscan streak camera equipped with a Chromex 250IS spectrograph
(4-nm spectral resolution, 3-ps time response). The streak images were
recorded on a Hamamatsu C4880 CCD camera, which was cooled to
255°C. Streak images were recorded on two different time scales (200 ps
and 2200 ps full range) and over a wavelength range of 315 nm, with the
detection polarizer oriented alternately parallel and perpendicular to the
vertically polarized excitation light. The polarization dependence of the
sensitivity of the apparatus was measured by recording streak images,
using horizontally polarized excitation light, with the polarizer in the
detection branch oriented both horizontally and vertically, and is expressed
in the so-called gfactor.
Global analysis
The measurements on both time scales and with both polarizations were
fitted simultaneously, using a global analysis program (van Stokkum et al.,
1994) for the wavelength region in which no scattering of the exciting laser
light was present. The two independent series of experiments were fitted
separately. Included in the fitting procedure is the signal that is detected in
the back sweep of the streak camera, which is 6–8 ns after the excitation
pulse. The experimentally determined gfactor was introduced into the
fitting procedure. In the model an initial anisotropy of 0.4 is assumed. The
amplitudes of the fitted kinetics are rather sensitive to small variations in
the gfactor; however, the variation in the corresponding time constants is
limited. For both data sets we have estimated the error margins for the
amplitudes by examining the consequences of small variations in the g
factor.
RESULTS
Absorption and fluorescence
In Fig. 1 the absorption (solid line) and fluorescence emis-
sion (dashed line) spectra of PCP at room temperature are
shown. The inset shows the overall absorption spectrum of
PCP at room temperature. The absorption band at 670 nm is
due to the Q
y
band of Chl aand has a FWHM of 14 nm. The
absorption in the 450–600-nm region is due to peridinin,
and the peak at 430 nm is due to the Soret band of Chl a.
The spectrum is very similar to the absorption spectra of
PCP reported before (Koka and Song, 1977; Carbonera et
al., 1996). In the time-resolved fluorescence emission ex-
periment the sample was excited at 660 nm (thick vertical
line in Fig. 1), and the anisotropy was calculated from the
fluorescence detected between 675 and 700 nm. The anisot-
ropy decay was independent of the detection wavelength.
The absorption and fluorescence emission spectra shown
FIGURE 1 Absorption spectrum (solid line) and fluorescence emission
spectrum (dashed line) of PCP at room temperature (excitation at 475 nm).
The excitation wavelength (5660 nm) used for the time-resolved anisot-
ropy measurement is indicated by a thick solid line. The inset shows the
overall absorption spectrum of PCP at room temperature.
Excitation Energy Transfer in PCP 345
Biophysical Journal 78(1) 344–353
here were used for the calculation of the Fo¨rster overlap
integral (see Appendix 2).
Time-resolved fluorescence anisotropy
In Fig. 2 the F
F
(t) and F
'
(t) components (polarization of
the detection being parallel and perpendicular to the vertical
polarization of the excitation light, respectively) of the
fluorescence emission spectra are plotted on a linear-loga-
rithmic time scale for the 200-ps window (Fig. 2 A) and for
the 2200-ps time window (Fig. 2 B). The detection wave-
length of these traces was 675 nm. At detection wavelengths
shorter than 675 nm, scattering of the excitation light con-
tributes at time scales on the order of the instrument re-
sponse. The anisotropy was independent of the detection
wavelength; therefore the 675–700-nm region was fitted
using a global analysis routine (van Stokkum et al., 1994).
The solid lines in Fig. 2 show the result of a simultaneous
fit of the F
F
(t) and F
'
(t) components in the two time
domains. In the fit procedure the anisotropy at t50 was
fixed at 0.4. Two decay time constants were needed to fit
the decay of the anisotropy r(t):
r~t!5A1e2t/
t
11A2e2t/
t
21r`50.24e2t/(6.860.8)
10.05e2t/(350615) 10.11 (1)
The two depolarization times
t
1
and
t
2
are tentatively in-
terpreted as intra- and intermonomeric equilibration times,
respectively. The error margins are estimated on the basis of
the fits of two independent series of experiments. The
estimated error margin of the amplitude of the fast process
(A
1
) is 0.24 60.02. The amplitude of the 350 615-ps
process could be estimated very accurately to be 0.05, and
the fitted amplitude of the residual anisotropy is anticorre-
lated to the fitted amplitude of the fast process. Therefore,
the amplitude of the residual anisotropy (r
`
) is 0.11 60.02.
On the time scale of the fastest depolarization process
hardly any depolarization due to the slower process takes
place. The anisotropy “after” the fast depolarization process
(r
1
) can be defined as r
1
50.4 2A
1
50.16 60.02.
Because the experiment is performed in water, one might
expect a third depolarization time constant caused by the
rotational motion of the PCP complex. The rotational de-
polarization time was reported to be 33 ns (Koka and Song,
1977). On the basis of the known size of the complex one
can calculate that the rotational depolarization time (Cantor
and Schimmel, 1980), is ;48 ns for the PCP trimer and
;16 ns for the monomer. Addition of an extra component
with a depolarization time constant of 16–48 ns in the
global analysis procedure did not lead to an improvement of
the fit, and therefore the rotational depolarization is negli-
gible.
The isotropic fluorescence decay time constant was esti-
mated to be ;4.2 ns, which is in reasonable agreement with
the fluorescence lifetime of 4.6 ns reported by Koka and
Song (1977).
DISCUSSION
Calculation of Fo¨ rster energy transfer rates
based on the structure of PCP
For the application of the Fo¨rster equation two prerequisites
should be fulfilled: 1) the dipole interaction approach
should be justified and 2) the excitonic coupling between
the pigments should be weak. In the case of PCP, the
center-to-center distance between the interacting pigments
is at least 17 Å, significantly larger than the conjugated part
of the porphyrin, so that the dipole-dipole approximation is
justified. The second constraint quantitatively implies that
the coupling between the pigments is smaller than the
homogeneous width of the absorption bands. The Chl aQ
y
band of PCP has a width of 300 cm
21
, and the coupling
between two Chl ain a PCP monomer is on the order of 10
cm
21
(Kleima, 1999), so the second condition is also ful-
filled.
On the basis of the crystal structure of PCP, the excitation
energy transfer rates can now be calculated using the Fo¨rster
equation (Fo¨rster, 1965):
kDA 5
k
2
R6z
kr
D
n4zI5
k
2
R6zC(2)
FIGURE 2 Time traces of the F
F
(t) and F
'
(t) components of the
fluorescence decay spectrum of 200 ps (A) and 2200 ps (B) time domains
measured at room temperature, plotted with the result of the fit (solid line).
The detection wavelength is 675 nm. Note that the time base is linear
around time zero (the location of the maximum of the instrument response)
and logarithmic in the range 20–200 ps (A) or 200–2000 ps (B).
346 Kleima et al.
Biophysical Journal 78(1) 344–353
with
I58.8 31017 z
E
e
A~
n
˜!zfD~
n
˜!
n
˜4d
n
˜(3)
Here k
DA
(ps
21
) is the rate of transfer from donor (D)to
acceptor (A),
k
is an orientation factor which is given below,
nis the refractive index, Ris the distance between the
centers of the interacting pigments in nm, and k
r
D
is the
radiative rate of the donor molecule (ps
21
). The integral
reflects the overlap between the fluorescence spectrum of
the donor normalized to area unity and the absorption spec-
trum of the acceptor scaled to the value of the extinction
coefficient (M
21
zcm
21
) in the absorption maximum, both
on a frequency scale (cm
21
). The orientation factor
k
is
given by
k
5~
m
ˆ1z
m
ˆ2!23~
m
ˆ1zr
ˆ12!~
m
ˆ2zr
ˆ12!(4)
where
m
ˆ
1
and
m
ˆ
2
are the normalized transition dipole mo-
ment vectors and rˆ
12
is the normalized vector between the
centers of pigments 1 (donor) and 2 (acceptor). The center
of the Chl amolecule is taken to be the center of gravity of
the four nitrogen atoms in the molecular structure of Chl a
(see Fig. 3, inset). In the literature one often encounters the
Fo¨rster radius (R
0
), which is related to Cvia R
0
6
5
k
2
zC/k
r
D
.
In Fig. 3 the positions of the six Chl amolecules in
trimeric PCP are shown (Hofmann et al., 1996). Pigments 1
and 2 are the interacting pigments in a monomer. On the
basis of the trimeric structure, two energy equilibration
processes can be expected: within the monomer and within
the trimer, respectively. From linear dichroism and absorp-
tion spectroscopy experiments at room temperature
(Kleima, 1999) it is concluded that the two Chl amolecules
that are bound per monomeric unit are essentially isoener-
getic, which is reasonable because the two pigments are
located in very similar environments.
Because the pigments are isoenergetic at room tempera-
ture, the intramonomeric equilibration rate (k
eqM
) is twice
the excitation energy transfer rate (k
eqM
5k
12
1k
21
5
2k
12
51/
t
eqM
, where k
nm
is the transfer rate from pigment
nto pigment mand
t
eqM
is the time constant for equilibra-
tion within the monomer). The intermonomeric equilibra-
tion rate (k
eqT
) is calculated as follows:
keqT 53k12334 53@0.5~k13 1k14!10.5~k23 1k24!# 51/
t
eqT
(5)
The indices refer to the pigments as shown in Fig. 3, and
t
eqT
is the time constant for equilibration within the trimer.
Because the equilibration within the monomer is fast, the
transfer rate from monomer 12 to monomer 34 (k
12334
)is
the sum of the average transfer rates from, respectively,
pigment 1 to pigments 3 and 4 and from pigment 2 to
pigments 3 and 4. The equilibration rate within a trimer is
three times the rate for transfer between two monomeric
subunits (see, e.g., Causgrove et al., 1988). We stress that
the ratio of the inter- and intramonomeric equilibration
times is independent of the radiative lifetime, the refractive
index, and the overlap integral, when it is assumed that
these are the same for the two equilibration processes. This
is a reasonable assumption because the surroundings of the
Chl aare very similar.
FIGURE 3 Organization of Chl a
in PCP. Chl a1 and 2 belong to one
monomer. The arrows indicate tran-
sition dipole moments. The r
nm
show
the distances between the different
pairs of Chl a. The inset shows the
structure of Chl a, the orientation of
the Q
y
transition dipole moment, and
the definition of
a
, which is the angle
between the xaxis and the Q
y
transi-
tion dipole moment. Note that the
transition dipole moment is oriented
parallel to the plane of the Chl a
molecule.
Excitation Energy Transfer in PCP 347
Biophysical Journal 78(1) 344–353
Detailed comparison of experimentally
determined and calculated transfer rates
To discuss the transfer processes in terms of the Fo¨rster
equation in detail, accurate knowledge of the Q
y
transition
dipole moment within the porphyrin plane is required. To a
first approximation the dipole is often taken to be along the
yaxis (see Fig. 3), but this is not entirely correct (see, e.g.,
van Zandvoort et al., 1995, and Appendix 1). In Fig. 3 the
angle
a
is defined, which corresponds to the angle between
the Q
y
transition dipole moment and the xaxis of the
molecular frame of Chl a. (Note that the yaxis corresponds
to the NB-ND axis of the Chl amolecule, whereas the xaxis
is perpendicular to the yaxis). Assuming that the prepara-
tion exclusively contains trimers, there are three experimen-
tally determined parameters available that depend on the
choice of
a
, which will be discussed below: 1) the amount
of anisotropy (r
1
) that remains after equilibration within the
monomer, 2) the residual anisotropy (r
`
) that remains after
equilibration within the trimer, and 3) the ratio
t
1
/
t
2
of the
equilibration within the monomer and trimer, respectively.
However, a complicating factor is the fact that the prepara-
tion does not only contain trimers. Using ultracentrifugation
techniques, it was shown that the percentage of PCP trimers
present in a preparation depends on the PCP concentration,
and, at the concentration applied in our experiments, one
expects the presence of both monomers and trimers (Hof-
mann et al., unpublished results). Because biochemical sep-
aration of the monomers and trimers affects the monomer/
trimer equilibrium, the exact percentages of monomers and
trimers at a certain initial PCP concentration are hard to
give. As a consequence, r
1
provides the most unambiguous
information about
a
because this term is independent of the
state of oligomerization (assuming that the relative orienta-
tions of the Chl molecules within the monomer are the same
in all cases).
The expected anisotropy after equilibration within the
monomer (r
eqM
) can be calculated using r
eqM
50.5(0.4 1
r
132
) with r
132
50.2 (3cos
2
f
12
21), where r
132
is the
anisotropy after 100% energy transfer from pigment 1 to
pigment 2 and
f
12
is the angle between the relevant tran-
sition dipole moments of the interacting pigments (see Fig.
3). The angle
f
12
depends on the orientation of the transi-
tion dipole moment within the molecular frame of the
chlorophyll molecule. In Fig. 4 Ar
eqM
is plotted as a
function of
a
. The vertical dashed line shows the value of
r
eqM
in the case where the transition dipole moments are not
rotated (
a
is 90°, parallel to the yaxis). The horizontal
dotted line shows the experimentally determined anisotropy
after equilibration within the monomer, and the gray area
reflects the error margin (r
1
50.16 60.02). Clearly, a
value of
a
589–94° leads to a good correspondence
between experiment and calculation. Other regions where
the experimental and calculated anisotropy are in agreement
are 9–15°, 57–63°, and 158–163°. However, we do not
expect that the transition dipole moment has an orientation
differing that much from the yaxis, because in, e.g., BChl
abound to protein,
a
is also close to 90°, as can be
concluded from modeling studies on LH2 (Koolhaas et al.,
1998) and the FMO complex (Louwe et al., 1997; Vulto et
al., 1999).
Subsequently, the expected residual anisotropy in the
case of trimers (r
eqT
) for
a
589–94° can be calculated,
assuming that in our sample all PCP is trimeric. A value
ranging between 0.04 and 0.05 is found for r
eqT
, which is
lower than the experimentally determined residual anisot-
ropy (r
`
50.11 60.02). A similar, relatively high value
was found in steady-state anisotropy measurements per-
formed both at room temperature and 4 K (unpublished
results). This shows that the assumption that the preparation
FIGURE 4 (A) The amplitude of the anisotropy “after” equilibration
within the monomer (r
eqM
) as a function of
a
. The vertical dashed line
indicates r
eqM
for
a
is 90° (Q
y
along the yaxis; see Fig. 3). The horizontal
dotted line gives the experimentally determined value, and the gray area
shows the error margin. (B) The calculated ratio
t
eqM
/
t
eqT
as a function of
the angle
a
. The vertical dashed line indicates that the ratio for
a
is 90°.
The horizontal dotted line gives the experimentally determined ratio, and
the gray area shows the error margin.
348 Kleima et al.
Biophysical Journal 78(1) 344–353
exclusively contains trimers is not correct. On the other
hand, if the preparation would contain only monomers, we
would not observe a slow depolarization time. Moreover,
the linear dichroism spectrum would be completely differ-
ent (Kleima, 1999). Obviously, the preparation consists of a
mixture, which is in line with the results of the ultracentrif-
ugation experiments (see above). For instance, assuming
that 50% of the total amount of Chl ais bound to trimers
and 50% is bound to monomers would explain the experi-
mental residual anisotropy. However, if trimers and mono-
mers are present and the aggregation is not entirely coop-
erative, the presence of dimers cannot be excluded, although
there are no biochemical indications that these indeed exist.
The ratio
t
1
/
t
2
is the third experimental parameter that
provides information about the energy transfer in PCP. This
ratio is not influenced by the presence of monomers, al-
though it is affected by the possible presence of dimers (see
below). At first, we will neglect the possible fraction of
dimers. In Fig. 4 Bthe calculated ratio
t
eqM
/
t
eqT
is shown as
a function of
a
. The asymptotes correspond to the case
where
k
for the intramonomer equilibration rate becomes
zero (
t
eqM
3`). The value for
k
can be positive or
negative, depending on the direction of the transition dipole
moment; however, because the transfer rate is proportional
to
k
2
, the period is 180°. The dashed line shows the ratio
t
eqM
/
t
eqT
, which is 0.038 for unrotated transition dipole
moments (
a
is 90°, parallel to the yaxis). The dotted line
shows the average value for the experimentally determined
ratio (
t
1
/
t
2
50.019 60.003), and the gray area reflects the
error margin. Correspondence between the experimentally
determined and calculated values is found for
a
597–105°.
Other regions are 60–65°, 139–142°, and 164–169°. How-
ever, as discussed above, these values are not realistic.
The discussion in the preceding paragraphs concerning
trimers (or monomers and trimers) is summarized in Fig. 5
A, where the amplitude of the anisotropy r
eqM
(dashed, right
y axis), the residual anisotropy r
eqT
(dotted, right y axis),
and the ratio
t
eqM
/
t
eqT
(solid, left y axis) are shown for
a
ranging from 80° to 110°. The ranges of
a
values (repre-
sented by gray areas) corresponding to the experimental
parameters r
1
and
t
1
/
t
2
do not overlap. The highest value
for
a
based on the experimentally determined value for r
1
is
a
594°, whereas the lowest value for
a
based on
t
1
/
t
2
is
a
597°.
Alternatively, if we assume that the preparation contains
only dimers (or dimers and monomers), which are organized
like trimers missing one monomeric unit, we can define the
residual anisotropy in the dimer (r
eqD
) and the ratio
t
eqM
/
t
eqD
, where
t
eqD
is the equilibration time constant within the
dimer (
t
eqD
51.5 3
t
eqT
). Fig. 5 Bis similar to Fig. 5 A, but
represents the case of dimers. In this case there is horizontal
overlap of the gray areas for
a
592–94°. The residual
anisotropy ranges from 0.075 to 0.09, which is in reasonable
agreement with the measured residual anisotropy. It should
be noted that trimers containing a Chl athat does not
transfer properly will also show a depolarization behavior
between those of dimers and trimers.
Summarizing, the data indicate that we do not have only
monomers (or trimers), and the data can be explained by the
exclusive presence of dimers, but this is in disagreement
with biochemical experiments. We are probably dealing
with a mixture of monomers, dimers, and trimers. Assuming
dimers (or dimers and monomers) implies that
a
592°–
94°, the simultaneous presence of trimers tends to favor the
slightly larger values of
a
.
It has been concluded by van Zandvoort et al. (1995) that
a
differs for absorption and emission. This is, in principle,
due to “solvent” relaxation, but it is demonstrated in Ap-
pendix 1 that for Fo¨rster transfer between isoenergetic pig-
ments one cannot simply use different values for
a
in the
case of absorption and emission, because this leads to a
FIGURE 5 (A) The ratio
t
eqM
/
t
eqT
(solid, left y axis) and the amplitude
(right y axis) of the anisotropy “after” equilibration within the monomer
(r
eqM
,dashed line) and the residual anisotropy (r
eqT
,dotted line) are plotted
versus
a
. The gray areas reflect the experimentally determined values of
the ratio
t
1
/
t
2
and the remaining anisotropy “after” equilibration within the
monomer (r
1
). (B) Same as in A, but in the case where the preparation
consists of 100% dimers,
t
eqD
reflects the time constant for equilibration
within the dimer and r
eqD
reflects the residual anisotropy.
Excitation Energy Transfer in PCP 349
Biophysical Journal 78(1) 344–353
conflict with the laws of thermodynamics. Nevertheless, in
the event of transfer between isoenergetic pigments the
value of
a
may in principle vary as a function of the
absorption/emission wavelength. If the variation exists, then
the values estimated above should be considered an effec-
tive (average) orientation.
Estimation of the refractive index
In the previous paragraph we have estimated, using the
experimentally determined values for the anisotropy r
1
and
the ratio
t
1
/
t
2
, the values of
a
that lead to agreement
between the experimental data and the calculations using
the PCP structure. With this information about
a
, the cal-
culated time constants
t
eqM
and
t
eqT
(and/or
t
eqD
) can be
scaled to “real” time constants, using the refractive index,
k
r
D
and the overlap integral, together forming the constant
part (C) of the Fo¨rster equation. In Appendix 2 this factor
(C) is determined. The radiative lifetime is estimated from
literature values for the fluorescence quantum yield and the
fluorescence lifetime of Chl a(Seely and Conolly, 1986),
leading to C542/n
4
ps
21
nm
6
for
t
r
D
518.5 ns (for details
see Appendix 2). The refractive index can be used for the
actual scaling of the calculated time constants to “real” time
constants.
In Table 1 the results are shown. We have examined the
consequences for the refractive index for both scaling to
t
1
(upper half of Table 1) and scaling to
t
2
(lower half of Table
1). The first column shows whether we assume trimers (and
monomers) or dimers (and monomers), the second column
gives the upper and lower limits of
a
as determined in the
previous paragraph, the third column gives the calculated
ratio
t
1
/
t
2
(for that particular
a
and the assumed composi-
tion of the preparation), and the fourth column gives the
experimentally determined upper and lower values of
t
1
.
The column with heading
t
2
presents the time constants
resulting from the values for the ratio and
t
1
in the same
row. In the next column the corresponding scaling factor is
shown. The last column shows the resulting values for n.
The lower part of Table 1 is the same as the upper part, but
in this case
t
2
represents the experimentally determined
value.
Clearly, the refractive indices required for proper scaling
of the time constants in the case where the preparation is
assumed to consist of trimers (and monomers) are higher
than those in the case of dimers (and monomers). The
average refractive index is 1.6 60.1, where the error
margins reflect the standard deviation. This value is signif-
icantly higher than the refractive index of the medium,
which is water in this case (n51.33). It was suggested by
Moog et al. (1984) that the refractive index in the Fo¨rster
equation should be interpreted as that of the bulk solution.
Our data are clearly not in agreement with that statement,
and the effect of the protein and/or the peridinins should be
taken into account. By very different methods, the refractive
indices of, for example, LH2 and CP47 have been deter-
mined to be 1.63 (Andersson et al., 1991) and 1.51 (Renge
et al., 1996), respectively.
To illustrate the dependence of the transfer rates between
individual pigments (numbering according to Fig. 3) on the
value of
a
, these rates are shown in Table 2 for
a
592° and
for
a
597°, using C542/n
6
ps
21
nm
6
and the average
value of n(51.6). In addition, the corresponding factors
k
2
/R
6
and the time constants are shown. The equilibration
time constant in the case of dimers with
a
592° is 438 ps,
whereas in the case of trimers with
a
597° we find 269 ps.
Note that the discrepancy with the experimental value is due
to the strong dependence of the transfer rates on n(see
Table 1).
We have shown here that the Chl ato Chl aexcitation
energy transfer in PCP can very well be modeled using the
Fo¨rster equation. The crystal structure, in which the molec-
ular frames of the Chl amolecules were resolved, enabled
us to estimate the orientation of the Q
y
transition dipole
moments and conclude that
a
594.5 62.5°. By using this
value of
a
, the experimentally determined excitation equil-
ibration time constants of 6.8 60.8 ps and 350 615 ps can
be assigned to equilibration times within the monomer and
within the trimer/dimer, respectively.
TABLE 1 Scaling of the calculated equilibration time
constants to the experimental time constants
Sample
a
(°)
t
1
/
t
2
calculated
t
1
(ps)
t
2
(ps) Scaling
factor n
Scaling to
t
1
Trimer 94 0.0272 6.0 221 8.148 1.51
7.6 279 6.432 1.60
97 0.0224 6.0 269 6.409 1.60
7.6 339 5.060 1.70
Dimer 92 0.0212 6.0 283 9.925 1.43
7.6 358 7.836 1.52
94 0.0181 6.0 331 8.148 1.51
7.6 420 6.432 1.60
Scaling to
t
2
Trimer 94 0.0272 9.1 335 5.370 1.67
9.9 365 4.928 1.71
97 0.0224 7.5 335 5.122 1.69
8.2 365 4.701 1.72
Dimer 92 0.0212 7.1 335 8.371 1.50
7.7 365 7.683 1.53
94 0.0181 6.1 335 8.055 1.51
6.6 365 7.393 1.54
Average n1.6 60.1
Scaling is based on the value of the first intramonomer equilibration time
t
1
(upper part) or on the slow intermonomer equilibration time
t
2
(lower
part). The first column shows whether trimers (and monomers) or dimers
(and monomers) are assumed, the second column gives the upper and lower
limits of
a
, the third column gives the calculated ratio
t
1
/
t
2
(for that
particular
a
and the assumed composition of the preparation), and the
fourth column gives the experimentally determined upper and lower values
of
t
1
. The column with the heading
t
2
shows the time constants resulting
from the values for the ratio and
t
1
in the same row. The next column
shows the corresponding scaling factor. The last column shows the values
for n(using C542/n
4
ps
21
nm
6
).
350 Kleima et al.
Biophysical Journal 78(1) 344–353
What can be said about the in vivo
functioning of PCP?
Because of the relatively slow energy transfer from one
monomer to the next within the PCP complex, one could
wonder whether this transfer will actually occur in vivo,
because other transfer processes might be faster. When two
trimeric PCP complexes are oriented favorably with respect
to each other, PCP-to-PCP transfer can be faster than the
intermonomeric transfer within one trimeric complex (Hof-
mann, manuscript in preparation). However, it is not very
likely that larger in vivo aggregates of PCP complexes are
formed, as suggested by Knoetzel and Rensing (1990),
because such aggregates have not been isolated and are not
formed upon crystallization. The probably more important
energy transfer processes that might compete with those
within the PCP complex are the transfer processes to the
membrane-bound PSII complex. However, it is not known
whether this transfer occurs via the LHCa/ccomplex (Hof-
mann et al., 1996), via the CP43 or CP47 complexes
(Mimuro et al., 1990), or directly to the PSII core complex
(Knoetzel and Rensing, 1990). Because the LHCa/ccom-
plex is to some extent similar to the LHCII complex of
green plants (Hiller et al., 1995), it might be modeled on the
basis of the crystal structure of LHCII (Ku¨hlbrandt et al.,
1994; Hofmann, unpublished results), and therefore it forms
the “easiest” candidate for some tentative calculations. The
PCP 3LHCa/ctransfer can be calculated by using this
model, the assignment of Chl aaccording to Ku¨hlbrandt et
al. (1994), and the orientations of transition dipole moments
according to Gradinaru et al. (1998), n51.6 and C542/n
6
.
If the trimer axis of PCP and LHCa/care aligned, the
orientation (in terms of rotation along the trimer axis) is as
favorable as possible, PCP and LHCa/care as close as
possible, and PCP is located on the luminal side, the shortest
transfer time from a PCP Chl ato a LHCa/cChl ais ;140
ps (Hofmann, manuscript in preparation). This is shorter
than the transfer time between two PCP monomers (;1 ns).
Including the (unfavorable) transfer from the other Chl ain
the PCP monomer and the transfer to other LHCa/cChl a
molecules, an average transfer time of ;150 ps is found in
this specific case. We thus might speculate that some trans-
fer to the LHCa/ccomplex competes with transfer between
monomers, although it should be emphasized that the num-
bers given here strongly depend on the modeling parameters.
APPENDIX 1: ROTATION OF TRANSITION
DIPOLE MOMENTS
It was concluded from angle-resolved fluorescence depolarization experi-
ments on Chl aoriented in nitrocellulose film that the transition dipole
moments for absorption and emission are not oriented parallel to each
other, but are at an angle of 17–19° with respect to each other (van
Zandvoort et al., 1995). The transition dipole moment for absorption was
found to be parallel to the Q
y
axis (
a
590°) of the Chl molecule, while the
transition dipole moment for emission is oriented at
a
is 107–109° in the
plane of the Chl molecule (see inset of Fig. 3). The time scale of this
rotation could easily be on the order of a few picoseconds because it might
be related to solvent (protein) relaxation processes that have been shown to
occur on such time scales in the case of Chl b(Oksanen et al., 1998) and
therefore could be of importance in photosynthetic complexes. Below we
will examine the consequences for Fo¨rster excitation energy transfer.
In Fig. 6 three imaginary photosynthetic complexes are shown. The
pigments are isoenergetic, and the transition dipole moments of each
pigment for absorption and emission are, respectively,
m
A
and
m
E
. In Fig.
6Atwo pigments are placed at rotationally symmetrical positions with
respect to the axis perpendicular to the plane of the paper. For excitation
energy transfer from pigment 1 to 2 the transition dipole moments
m
1E
and
m
2A
are involved, while for transfer from 2 to 1
m
2E
and
m
1A
are involved.
Because of the symmetrical position of the pigments with respect to each
other,
k
132
2
equals
k
231
2
, so that back and forward excitation energy
transfer rates are the same. In Fig. 6 Ban asymmetrical dimer is shown.
Because in this case the angle between
m
3E
and
m
4A
is not the same as the
angle between
m
4E
and
m
3A
, it follows that
k
334
2
is not equal to
k
433
2
.
Therefore, in equilibrium relatively more excitations would be located on
pigment 3 than on pigment 4, although the pigments are isoenergetic. In
Fig. 6 Ca symmetrical trimeric structure is shown. In the trimer the
pigments 5 and 6 are at the same positions with respect to each other as the
pigments 3 and 4. As a consequence, the transfer from pigment 6 to 5 is
faster than that from pigment 5 to 6, and the same holds for the pigment
pairs 5–7 and 7–6. In other words, in the case of three isoenergetic
pigments with different orientations of the transition dipole moments for
absorption and emission, the excitation would continuously circle around,
which seems counterintuitive.
In the case of isoenergetic pigments in the asymmetrical dimer, the
unidirectionality of transfer is thermodynamically impossible. Apparently,
rotation of the transition dipole moment in the excited state cannot occur
without affecting the energy of the excited state. In other words, it is no
longer correct to assume that the energy of the pigment in the excited state
and the orientation of the transition dipole moment are independent prop-
erties. An explanation for this feature is that the rotation of the transition
dipole moment might be caused by solvent reorganization effects, in
general leading to a lowering of the energy of the excited state. Fo¨rster
excitation energy transfer only takes place when the corresponding instan-
taneous donor and acceptor transition energies are the same. As a conse-
quence, formally the orientation factor in the Fo¨rster equation becomes
TABLE 2 Calculated rates and time constants for transfer
between individual pigments in PCP
Pigments #,#
k
2
/R
6
(nm
26
)k(ps
21
)
t
a
592°
1,2 8.396*10
23
0.054 18.6 ps
1,3 6.278*10
25
4.023*10
24
2.49 ns
1,4 2.222*10
24
1.424*10
23
0.70 ns
2,3 1.054*10
25
6.755*10
25
14.8 ns
2,4 6.107*10
25
3.914*10
24
2.56 ns
a
597°
1,2 0.013 0.083 12 ps
1,3 7.061*10
25
4.525*10
24
2.21 ns
1,4 2.539*10
24
1.627*10
23
0.61 ns
2,3 1.533*10
25
9.823*10
25
10.2 ns
2,4 4.875*10
25
3.124*10
24
3.20 ns
The calculated factors
k
2
/R
6
, the transfer rates, and the transfer times are
shown for
a
592° and for
a
597°. Pigments are numbered as indicated
in Fig. 3. A refractive index of 1.6 was used, and Cwas 42/n
4
ps
21
nm
6
.
Excitation Energy Transfer in PCP 351
Biophysical Journal 78(1) 344–353
energy dependent and therefore has to be included in the overlap integral:
kDA 58.8 31017 z
kr
D
R6n4z
E
k
2~
n
˜!
e
A~
n
˜!fD~
n
˜!
n
˜4d
n
˜
In conclusion, when one allows different orientations of the transition
dipole moments for absorption and emission, one should evaluate the
above expression. In the case of PCP we have considered the situation
where the transition dipole moments for absorption and emission are
parallel, but we have rotated the transition dipole moment over an angle
a
with respect to the molecular frame. The value for
a
is taken to be the same
for all pigments. Thus the angle should be considered as an effective
“average” angle.
APPENDIX 2
Below the constant factor in the Fo¨rster equation, consisting of the overlap
integral and the radiative rate, is calculated.
To calculate the overlap integral in the Fo¨rster equation, the extinction
coefficient of PCP in the Chl aQ
y
band has to be estimated. To that end
the absorption spectrum of the Q
y
band in PCP has been compared to that
of Chl ain different solvents with known extinction coefficients. The
FWHM of the Q
y
band in the OD spectrum of PCP is 14 nm (see Fig. 1).
The extinction coefficients and FWHMs of the Q
y
band of Chl aare 90.25
mM
21
cm
21
in ether (FWHM 17 nm; Lichtenthaler, 1987), 79.6 mM
21
cm
21
in 100% methanol (FWHM 22 nm; Eijckelhoff and Dekker, 1995),
and 86 mM
21
cm
21
in aqueous acetone (FWHM 20 nm; Eijckelhoff and
Dekker, 1995) (Lichtenthaler, 1987; Porra et al., 1989). Assuming that the
dipole strengths of Chl ain PCP and in these solvents are the same, we
have normalized the areas of the absorption spectra with respect to each
other in the Q
y
region and thus estimated the extinction coefficient of Chl
ain PCP to be ;110 mM
21
cm
21
.
The radiative rate in the Fo¨rster equation is estimated by using k
r
D
5
f
f
/
t
f
, where
t
f
is the fluorescence lifetime and
f
f
is the quantum yield for
fluorescence. Using literature values for
t
f
and
f
f
for Chl ain methanol and
in ether, we find an average radiative lifetime of 18.5 ns (Seely and
Conolly, 1986). So for Cwe find a value of 42/n
4
ps
21
nm
6
.
The authors thank Dr. Marc van Zandvoort and Drs. Markus Wendling for
useful discussions and Dr. Roger Hiller for providing us with the unpuri-
fied PCP material.
This work was supported by a Dutch Science Foundation FOM grant to
HvA and RvG.
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Excitation Energy Transfer in PCP 353
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