Carotenoid to chlorophyll energy transfer in light

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Chemical Physics Letters 379 (2003) 305–313
www.elsevier.com/locate/cplett
Carotenoid to chlorophyll energy transfer in light
harvesting complex II from Arabidopsis thaliana probed
by femtosecond fluorescence upconversion
Nancy E. Holt a, J.T.M. Kennis b, Luca DallÕOsto c,
Roberto Bassi c, Graham R. Fleming a,*
a
c
Department of Chemistry, University of California, Berkeley and Physical Biosciences Division,
Lawrence Berkeley National Laboratory, Berkeley, CA 94720-1460, USA
b
Department of Biophysics and Physics of Complex Systems, Division of Physics and Astronomy, Faculty of Sciences,
Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
Dipartimento Scientifico e Tecnologico, Facolt
a di Scienze, Universit
a di Verona, Strada Le Grazie, I-37134 Verona, Italy
Received 1 July 2003; in final form 24 July 2003
Published online: 12 September 2003
Abstract
Trimers of light harvesting complex II from Arabidopsis thaliana were studied by femtosecond fluorescence upconversion. The average lifetime of the carotenoid S2 state was 57 fs for wild type trimers and 70 fs for trimers from
a mutant plant with a distinctly different carotenoid composition. We estimate that 56% of the energy transferred
from carotenoids to chlorophylls proceeds via the carotenoid S2 state in the wild type and 46% in the mutant. By
comparison with the fluorescence excitation spectra, we find that 20% of the energy transferred in both samples
proceeds through the carotenoid S1 state.
Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction
The single most important protein for coloring
the world is light harvesting complex II (LHCII)
from green plants. Its function is as important as
its color is prevalent. LHCIIÕs dominant and
most well defined role is to collect solar energy
*
Corresponding author. Fax: +510-642-6340.
E-mail address: grfleming@lbl.gov (G.R. Fleming).
and transfer it to the photosystem II (PSII) reaction center, where it is used to drive the primary charge separation of the water splitting
reaction of photosynthesis. Isolated LHCII exists
in trimeric form and is comprised of subunits
from the lhcb1–3 gene products [1]. Each monomer contains 5–6 chlorophyll (Chl) b, 7–8 Chl a,
and at least three carotenoids (Cars), each associated with a specific binding site. Wild type (WT)
trimers have lutein (Lut) bound to the L1 site, a
4:1 mixture of Lut to violaxanthin (Vio) in the L2
0009-2614/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2003.08.039
306
N.E. Holt et al. / Chemical Physics Letters 379 (2003) 305–313
site and neoxanthin (Neo) bound to the N1 site.
A fourth site (V1), whose exact location is unknown but is somewhere on the periphery of the
complex, binds violaxanthin (Vio) in substoichiometric amounts. The Vio bound in the V1
site cannot transfer energy to Chl [2,3]. Trimers
obtained from the npq2 mutant plant lack carotenoids that are biosynthetically derived from
zeaxanthin (Zea), namely antheraxanthin, Vio
and Neo, due to a defect in the Zea epoxidase
enzyme [4]. The npq2 LHCII trimers bind 3 Cars,
L1 binds Lut and L2 binds a 1:1 mixture of Lut
to Zea. The N1 binding site is empty due to the
lack of Neo. The V1 site binds Lut [5].
The overall energy transfer efficiency from Cars
to Chl in HIILC of 80% is among the highest in
green plant antenna proteins [6–8]. There is general consensus that the dominant portion of the
energy (estimates range from 50% to 80% [9–11]) is
transferred from the Car state with approximate
1 þ
Bu symmetry, generally referred to as the second
singlet excited state (S2 ). The S2 state shows strong
one photon absorption from 400–550 nm. The
first singlet excited state (S1 ) of Cars does not
appear in the linear absorption spectrum because
it has approximately the same symmetry as the
ground state ð1 A
g Þ. The exact role of the S1 state
in light harvesting in LHCII is still a subject of
debate [12–14].
Various studies have specifically addressed the
efficiency of energy transfer from the Car S2 to the
Chl Qx and Qy states in a variety of LHCII complexes. Femtosecond transient absorption (TA)
spectroscopy was employed in a number of these
studies [7,9,10,15]. Two previous studies used the
time resolved femtosecond fluorescence upconversion method [11,13]. In principle, the information obtained from upconversion and TA
measurements under similar excitation conditions
should agree, however, significant discrepancies
exist between measurements by the two different
techniques and between some measurements performed with the same technique. In this Letter, we
employ the femtosecond upconversion technique
with higher time resolution (IRF of 100 fs) than
the previous upconversion measurements to clarify
understanding of Car to Chl energy transfer in
LHCII.
2. Materials and methods
LHCII trimers were isolated from WT and npq2
plants of Arabidopsis thaliana. The plants were
grown in a growth chamber with a 12 h (25 °C)/12
h (20 °C) light/dark cycle for 5–6 weeks. Thylakoid
membranes were isolated according to Bassi et al.
[16], washed in EDTA, resuspended in distilled
water at a Chl concentration of 2 mg Chl/ml and
mixed with the same volume of 2% n-dodecyl bmaltoside (DM). After 15 minutes of solubilization
on ice with occasional stirring, the solution was
centrifuged at 40 000g for 10 min. The supernatant
was loaded onto a 0.1–1 M sucrose gradient (10
mM Tricine and NaOH, pH 8.5, and 0.006% DM)
and centrifuged at 256 000g for 17 h. The second
green band from the top, which contained pure
LHCII trimers, was harvested with a syringe,
concentrated to an optical density (OD) of 0.3/
mm at 490 nm, frozen in liquid nitrogen and stored
at )80 °C.
The samples were thawed immediately prior to
experiments with the exception of the LHCII WT
Chl fluorescence measurements, which were carried out on the following day after storage at 4 °C
in darkness overnight. An oxygen scavenging system (20 mM glucose, 0.038 mg/ml catalase (Sigma
C-100) and 0.1 mg/ml glucose oxidase (Sigma
G-6125)) was added to the samples to maintain
anaerobic conditions [17]. The samples were continually flowed and cooled (6–8 °C) during the
measurements. Absorption spectra taken before
and after each measurement (Shimadzu UV-1601)
showed no noticeable differences from each other
and from the original absorption spectrum measured immediately after the LHCII WT and npq2
isolation.
The deconvolution of the Soret region of the
absorption spectra (SLM-Aminco DW-2000
spectrophotomer) for both the LHCII WT and
npq2 trimers into the absorption spectra of its
constituent isolated pigments was carried out according to the method of Croce et al. [18]. The
deconvolution of the corrected fluorescence excitation spectra (Jasco FP-777 spectrofluorimeter)
for both samples in terms of their individual pigments has been described previously [19]. The detection wavelength for the fluorescence excitation
N.E. Holt et al. / Chemical Physics Letters 379 (2003) 305–313
spectra was 682 nm with a slit width of 3 nm. The
Chl a=b ratio for both samples were determined by
the method of Porra et al. [20].
b-carotene (Sigma 22040) was dissolved in nhexane (OmniSolv, 98.2%). Lutein and zeaxanthin
were supplied by Hoffman La Roche, Ltd. and
dissolved in toluene (Aldrich, 99.5%). Spirilloxanthin (Spx) was isolated by the method of
Cogdell et al. [21] and dissolved in n-hexane. The
measurements were preformed at room temperature (22 °C) on samples with an OD of 0.3/mm at
490 nm.
Femtosecond fluorescence upconversion experiments have been described previously [22–24].
Briefly, a Ti:sapphire oscillator (Coherent MIRA
Seed) was used to seed a regenerative amplifier
(Coherent RegA 9050) with external stretcher/
compressor which pumped an OPA, optical parametric amplifier (Coherent 9450). The OPA produced excitation pulses centered at 490 nm with a
pulse energy of 5 nJ, a repetition rate of 250 kHz,
and a temporal FWHM of 50 fs. A portion
(30%) of the 800 nm compressor output was used
as the upconversion gate beam. The sample, contained in a custom, 1 mm path length flow cell
(Starna Inc.), was placed at one focus of the elliptical mirror. The spontaneous emission from the
sample was collected by the mirror and upconverted with the gate beam at the mirrorÕs second
focus in a BBO Type I crystal (Inrad, thickness ¼ 0.25 mm, h ¼ 28:7°). A lens was use to
collect the upconverted signal, which was directed
into a double grating monochromator (Spex 1680)
and detected by a photomultiplier tube using gated
photon counting (Stanford Research Systems
SRS400).
For measurements of the Car S2 fluorescence,
the polarization of the pump beam was parallel
with respect to the gate beam. Chl fluorescence
measurements were preformed with the respective
polarizations of the pump and gate beam at magic
angle (54.7°). Polarizations were set with an achromatic polarizer placed in the pump beam (CVI
ACWP-400-700-10-2).
The IRF is generally well described by a
Gaussian function fitted to the pure Raman scattering signal of the solvent in exactly the same
experimental configuration used to measure the
307
Chl/Car S2 fluorescence. The IRF ranged from
100 fs (buffer) to 150 fs (n-hexane/toluene). In
the case of Spx, the n-hexane Raman scattering
was used as the IRF.
Single and biexponential fits of the Car S2 lifetime with a Gaussian IRF were carried out by two
nonlinear least squares fitting programs, Foppefit
and Spectra (S. Savikhin Software, Ames, IA). The
Spectra program was also used to fit the Spx Car
S2 lifetime with the n-hexane IRF and to perform
global analysis on the Chl fluorescence data.
3. Results
The full absorption spectrum of the WT and
npq2 LHCII trimers is shown in Fig. 1. The deconvolution and corresponding fit of the Soret
region of the absorption and fluorescence excitation spectra is shown for the WT in Fig. 2(a) and
(b), respectively and for the npq2 mutant in
Fig. 2(c) and (d), respectively. In the WT fits, only
three Car molecules are considered, Lut in both
sites L1 and L2, and Neo in site N1. Due to the
substoichiometric amount of Vio in the complex,
its contribution was not considered in the fitting.
The npq2 complex also binds three Cars, in the fits
they are Lut in sites L1 and V1, and Zea in site L2.
The Chl a=b ratio for both samples is 1.30, implying 7.4 Chl a and 5.6 Chl b per LHCII
monomer since each monomer contains 13 Chls
[25]. Two distinct Chl a spectral forms and three
distinct Chl b spectral forms were necessary to
obtain a best fit of the Soret region of the absorption and excitation spectra for both samples.
By comparison of the absorption and excitation
spectra, we find that the overall transfer efficiency
from Cars to Chl is 76% and 63% in the WT and
npq2 trimers, respectively. The efficiency of energy
transfer from Chl b to Chl a is 98% for both
complexes.
The femtosecond fluorescence decay kinetics at
560 nm upon excitation at 490 nm of Lut and Zea
in toluene and the WT and npq2 LHCII trimers,
along with their corresponding single exponential
fits, are shown in Fig. 3. Deconvolution of the
fluorescence measured for b-carotene in toluene,
cyclohexane and n-hexane with a Gaussian IRF
308
N.E. Holt et al. / Chemical Physics Letters 379 (2003) 305–313
Fig. 1. (a) Absorption spectra of the WT (solid line) and npq2 (dashed line) normalized at the absorption maximum of the Chl Qy
band.
2000000
2000000
abs
a1
a2
b1
b2
b3
neo
lute1
lute2
fitting
1600000
Absorption
1400000
1200000
1000000
800000
WT trimer excitation
1800000
1400000
1200000
1000000
800000
600000
600000
400000
400000
200000
200000
0
420
440
460
480
500
0
520
420
440
Wavelength (nm)
460
480
500
520
Wavelength (nm)
(c)
(d)
2000000
2000000
1600000
1400000
1200000
1000000
800000
1800000
1400000
1200000
1000000
600000
400000
400000
200000
200000
420
440
460
480
500
520
fitting
800000
600000
0
ex
a1
a2
b1
b2
b3
zea
lute1
npq2 trimer excitation
1600000
Excitation
abs
a1
a2
b1
b2
b3
zea
lute1
lute2
fitting
npq2 trimer absorption
1800000
Absorption
ex
a1
a2
b1
b2
b3
neo
lute1
lute2
fitting
1600000
Excitation
WT trimer absorption
1800000
0
420
440
460
480
500
520
Fig. 2. Deconvolution of the Soret region of the absorption and fluorescence excitation spectra for the WT trimers (a) and (b), respectively and npq2 trimers (c) and (d), respectively in terms of the absorption of individual pigments: Chls a (dotted lines), Chls b
(short-dash lines) and Cars (long-dash lines). The experimental absorption/excitation (solid line) is compared with the reconstituted
spectra obtained by summing the absorption/emission of the individual pigments (dot-dash line).
N.E. Holt et al. / Chemical Physics Letters 379 (2003) 305–313
309
1.0
Normalized counts
0.8
0.6
LHCII npq2 trimers
LHCII WT trimers
0.4
Lutein
Zeaxanthin
0.2
0.0
-200
0
200
400
600
800
Fig. 3. Femtosecond fluorescence decay traces for Lut and Zea in toluene, and npq2 and WT trimers upon excitation at 490 nm and
detection at 560 nm (circles) and their corresponding single exponential fits (solid lines). A Gaussian IRF of 100 fs is also shown
(dashed line).
gave single exponential S2 lifetimes of 144, 166 and
172 fs, respectively (data not shown). Within the
experimental error of 10 fs, these values are
identical to those obtained previously [26]. The S2
lifetime for Lut and Zea is 158 and 146 fs, respectively. Single exponential fits of the LHCII
trimers gave a value of 57 fs (WT) and 70 fs (npq2),
however, a slightly poorer fit was achieved than
with the Cars in solution. A biexponential fit of the
LHCII data gave components of 28 fs (92%) and
114 fs (8%) for the WT and components of 35 fs
(89%) and 130 fs (11%) for the npq2 mutant.
In previous spontaneous emission data from a
light harvesting protein which could not be adequately characterized by a single exponential fit,
the faster lifetime obtained from a biexponential fit
was interpreted as the average S2 lifetime of the
Cars that transfer energy to Chl, while the slower
exponential was postulated to arise from either
disconnected Cars in the sample or from excited
Cars associated with triplet Chl molecules [27]. To
test if these assumptions could reasonably explain
the apparent nonexponential decay observed for
the LHCII trimers, we measured the S2 fluores-
cence from spirilloxanthin (Spx), the carotenoid
with the shortest reported S2 lifetime, in n-hexane
under identical conditions as the LHCII measurements, since a Car in solution should not show
the distribution of lifetimes that may be expected
in protein samples. The Spx data showed improved fits similar to those obtained for the LHCII
trimers when a biexponential form was used instead of a single exponential function. Convoluting the n-hexane Raman scattering response, not
its fit, recorded immediately prior to the Spx
measurement, however, produced a good quality
single exponential fit with a decay time of 68 fs,
experimentally identical to the single exponential
decay time obtained by using a Gaussian IRF. The
quality of the single exponential fit with the nhexane IRF (Fig. 4(a)) was equivalent to the biexponential fit with a Gaussian IRF (Fig. 4(c)) and
significantly better than the single exponential fit
with a Gaussian IRF (Fig. 4(b)). Therefore, we
conclude that the apparent nonexponential decay
encountered for LHCII is an experimental artifact
and that the average S2 lifetime of the Cars in the
WT and npq2 trimers is well characterized by their
310
N.E. Holt et al. / Chemical Physics Letters 379 (2003) 305–313
0.30
1.0
0.25
0.20
0.15
0.8
Normalized Counts
0.10
0.05
0.6
0.00
250
300
350
400
450
500
15
Residual
0.4
10
5
0
-5
0.2
-10
250
300
350
400
450
500
Time (fs)
0.0
-200
0
200
400
600
800
1000
Time (fs)
(c)
0.30
0.30
0.25
0.25
Normalized Counts
Normalized Counts
(b)
0.20
0.15
0.10
0.05
0.15
0.10
0.05
0.00
0.00
250
300
350
400
Time (fs)
450
500
250
15
15
10
10
Residual
Residual
0.20
5
0
-5
300
350
400
Time (fs)
450
500
5
0
-5
-10
-10
250
300
350
400
450
500
250
300
350
400
450
500
Fig. 4. (a) Single exponential fit (solid line) of Spx in n-hexane (circles) convoluted with the n-hexane Raman scattering (dashed line).
Upper inset shows the same plot expanded in the time region of 220–500 fs and the lower insert shows the fit residuals (squares). (b)
Upper plot: single exponential fit (solid line) of Spx in n-hexane (circles) convoluted with a Gaussian IRF; lower plot: residuals
(squares). (c) Upper plot: Biexponential fit (solid line) of Spx in n-hexane (circles) convoluted with a Gaussian IRF; lower plot: residuals (squares).
single exponential fit parameters. (See Table 1 for
a summary of all fitting results).
Measurements of WT Chl fluorescence upon
excitation at 490 nm detected at three wavelengths,
655, 678 and 686 nm along with their corre-
sponding fits obtained by global analysis are
shown in Fig. 5 and summarized in Table 2. The
minimum number of exponential functions necessary to fully characterize the data set was four,
with time constants of 90 fs, 350 fs, 5 ps and
N.E. Holt et al. / Chemical Physics Letters 379 (2003) 305–313
Table 1
Fluorescence lifetimes for Cars upon excitation at 490 nm and
detection at 560 nm by means of a single exponential or biexponential fit with a Gaussian IRF, unless otherwise specified
s1
(fs)
A1
(%)
s2
(fs)
A2
(%)
b-carotene (toluene)
b-carotene (n-hexane)
b-carotene (cyclohexane)
Lutein (toluene)
Zeaxanthin (toluene)
Spirilloxanthin (n-hexane)
144
166
172
158
146
69
31
68
57
28
70
35
100
100
100
100
100
100
90
100
100
92
100
89
–
–
–
–
–
–
100
–
–
114
–
139
–
npq2 LHCII trimers
150
100
λdet=655 nm
50
–
–
–
–
10
–
–
8
–
11
Lifetimes are within 10 fs.
Biexponential amplitudes are within 5%.
0
0
1
2
Time (ps)
3
4
140
120
Counts
(IRF, n-hexane response)
WT LHCII trimers
200
Counts
Sample
311
100
80
60
40
λdet=678 nm
20
4. Discussion
The average Car S2 lifetime of the WT and npq2
LHCII trimers of LHCII is 57 and 70 fs, respectively. By means of TA spectroscopy and recombinant proteins, Croce et al. found decays in
the Car S2 region and rises in the Chl b bleaching
with very similar kinetics upon excitation at 490
nm [9]. Lifetimes of 50–90 fs were observed, in
good agreement with our measurements. From
our results, we can estimate the lifetime and efficiency of energy transfer from the Car S2 state to
Chl, which includes all of the energy accepting
states of both Chl a and Chl b. The rate of energy
transfer from a specific Car S2 state to Chl, kET2 ,
can be calculated from the formula, kET2 ¼ kS2 kIC , where kS2 is the rate of decay of the Car S2
state in the energy transfer complex and kIC is the
internal conversion (IC) rate of the Car S2 state
under identical conditions in the absence of energy
0
0
1
2
Time (ps)
3
4
300
250
Counts
> 100 ps. Although it is by no means obvious that
simple physical significance can be assigned to
each of these time constants, at the present level of
knowledge of the LHCII structure a simple, linear,
multistep energy transfer scheme seems to be an
appropriate model.
200
150
100
50
λdet=686 nm
0
0
1
2
3
4
Fig. 5. Chl fluorescence (circles) and the fits obtained by global
analysis (solid lines) upon excitation at 490 nm and detection at:
(a) 655 nm; (b) 678 nm; (c) 686 nm. The fluorescence observed
at 655 nm is predominantly from Chl b molecules, while the
fluorescence at 678 nm and 686 nm is mainly emitted from Chl a
molecules. A Gaussian IRF of 100 fs is also shown (dashed
lines).
transfer. The efficiency of energy transfer from the
Car S2 state to Chl, uS2 , can be calculated from the
equation, uS2 ¼ kET2 =ðkET2 þ kIC Þ. The average
1
energy transfer lifetime, sET2 ð¼ kET2
Þ from the Car
S2 state to Chl in the WT trimers is 90 fs if the
1
Car IC lifetime, sIC ð¼ kIC
Þ, is represented by Lut
312
N.E. Holt et al. / Chemical Physics Letters 379 (2003) 305–313
Table 2
Global analysis of WT LHCII Chl fluorescence upon excitation
at 490 nm
Detection
wavelength
655
678
686
s1 ¼ 90
(fs)
s2 ¼ 350
(fs)
s3 ¼ 5
(ps)
s4 > 100
(ps)
A1 %
A2 %
A3 %
A4 %
)100
)39
)30
39
)61
)48
33
2
)22
28
98
100
in toluene (sIC ¼ 158 fs) and 102 fs if sIC is represented by Lut in benzyl alcohol (sIC ¼ 130 fs
[11]). Previous measurements suggest that the Car
environment in LHCII is highly polarizable,
therefore, benzyl alcohol (index of refraction,
n ¼ 1:54) probably provides a more accurate description of the protein environment than toluene
(n ¼ 1:50). As a result, all subsequent values of
sET2 and uS2 are calculated with respect to sIC of
Lut in benzyl alcohol. sET2 for the npq2 trimers is
152 fs. uS2 is 56% and 46% for the WT and npq2
trimers, respectively.
Measurements of the Chl b fluorescence show a
single exponential rise of 90 fs, somewhat longer
than the value of sS2 measured by means of upconverting the Car S2 fluorescence. Since such fast
rises in Chl fluorescence are generally convoluted
with spectral cooling and Chl internal conversion
components, it is not possible to unequivocally
assign all of the sources of the 90 fs rise; however, it is in general agreement with direct Car S2
to Chl energy transfer. From the deconvolution of
the absorption spectra we find that upon excitation at 490 nm, 25% of the total Chl b (and a
negligible amount of Chl a) in the sample is directly excited. In addition, all three Cars are almost evenly excited at this wavelength. Previous
TA measurements utilized two different excitation
wavelengths, 490 and 500 nm, the later which
excites, for all intents and purposes, no Chl a/b.
At both wavelengths very pronounced rises in Chl
b bleaching were observed that appeared to be
well correlated with the Car S2 decays, indicating
that Car to Chl energy transfer should be clearly
observable even in the presence of a small amount
of direct Chl b excitation [9]. The ultrafast rise
component also appears in the Chl a fluorescence
traces in good agreement with previous measurements of direct Car to Chl a transfer [9,10,15].
The other time constants obtained have been
previously assigned as Chl b/a to Chl a electronic
energy transfer [7,9,28] and, therefore, justify the
linear kinetic scheme we assumed in our data
analysis. The 350 fs component has larger amplitude in both of the Chl a fluorescence traces
with respect to the Chl b trace. Therefore, in addition to Chl b to Chl a electronic energy transfer
this time constant may also be related to transfer from Car S1 hot states to Chl a which was
previously reported to occur on a timescale of
250 fs [13].
Combining steady-state and time resolved
spectroscopy, we find an overall Car to Chl energy
transfer efficiency of 76% for WT trimers, 56%
transferred directly from the Car S2 state, leaving
the other 20% to proceed via the Car S1 state. The
energy transfer efficiencies from the Car S2 and
Car S1 states to Chl obtained in this work are
experimentally identical to the values obtained by
Gradinaru et al. from TA measurements on WT
LHCII spinach trimers [10]. For the npq2 trimers,
the overall efficiency is 63% with 46% and 17%
being transferred from the Car S2 and Car S1
states, respectively.
5. Conclusion
The consistency of our spontaneous emission
results and the TA measurements of Croce et al.,
the most detailed study on LHCII to date, represent the first agreement between upconversion
and TA measurements on the Car S2 lifetime in
LHCII, and should provide a benchmark against
which to judge the quality of theoretical calculations of LHCII energy transfer dynamics.
Furthermore, the range of values obtained for
lifetime of the Car S2 state enforces the need for
more standardized experiments in order to fully
understand the more subtle details of the LHCII
protein. These details may hold the key to the
reason for the exchange of Cars, namely Vio to
Zea, under conditions where the light energy
absorbed exceeds a plants capacity for carbon
fixation [29].
N.E. Holt et al. / Chemical Physics Letters 379 (2003) 305–313
Acknowledgements
This work was supported by the Director, Office
of Science, Office of Basic Energy Sciences,
Chemical Sciences Division, of the US Department of Energy under contract number DE-AC0376SF00098. We thank Hoffmann La-Roche Ltd.
for the generous gift of lutein and zeaxanthin. We
also thank Roberta Croce (CNR Institute for
Biophysics, Milan, Italy) for advice on spectral
deconvolution. J.T.M.K. was supported by a
short-term fellowship from the Human Frontier
Science Program Organization.
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