Báo cáo khoa học: Kinetics of the quinone binding reaction at the QB site of reaction centers from the purple bacteria Rhodobacter sphaeroides reconstituted in liposomes docx

Kinetics of the quinone binding reaction at the
Q
B
site of reaction
centers from the purple bacteria
Rhodobacter sphaeroides
reconstituted in liposomes
Francesco Milano
1
, Angela Agostiano
1,2
, Fabio Mavelli
2
and Massimo Trotta
1
1
CNR, Istituto per i Processi Chimico-Fisici – Sezione di Bari and
2
Dipartimento di Chimica, Universita
´
di Bari, Italy
Transmembrane proton translocation in the photosynthetic
membranes of the purple bacterium Rhodobacter sphaero-
ides is driven by light and performed by two transmem-
brane complexes; the photosynthetic reaction center and the
ubiquinol–cytochrome c oxidoreductase complex, coupled
by two mobile electron carriers; the cytochrome and the
quinone. This paper focuses on the kinetics and thermo-
dynamics of the interaction between the lipophylic electron
carrier ubiquinone-10 and the photosynthetic enzyme
reconstituted in liposomes. The collected data were simula-

ted with an existing recognized kinetic scheme [Shinkarev,
V.P. & Wraight, C.A. (1993) In The Photosynthetic Reac-
tion Center (Deisenhofer, J. & Norris, J.R., eds.), pp. 193–
255. Academic Press, San Diego, CA, USA] and the kinetic
constants of the uptake (7.2 · 10
7
M
)1
Æs
)1
)andrelease
(40 s
)1
) processes of the ligand were inferred. The results
obtained for the quinone release kinetic constant are com-
parable to the rate of the charge recombination reaction
from the state D
+
Q
A
–
. Values for the kinetic constants are
discussed as part of the overall photocycle, suggesting that its
bottleneck may not be the quinone uptake reaction in
agreement with a previous report (Gerencser, L., Laczko, G.
&Maro
´
ti, P. (1999) Biochemistry 38, 16866–16875).
Keywords: reaction center; quinone binding; liposomes;
photosynthesis.

4
The photosynthetic apparatus of the nonsulfur purple
bacterium Rhodobacter sphaeroides sits primarily in dedica-
ted portions of the cell membrane called intracytoplasmatic
membranes (ICM) [1,2]. The key enzymes involved in the
build-up of the transmembrane proton gradient [3,4] that
eventually trigger ATP synthesis [5] are located in the ICM.
The increase in the photosynthetic transmembrane proton
gradient occurs following absorption of solar electromag-
netic radiation, which is performed by light harvesting
complexes (LHCs) [6,7]. The LHCs channel excitons to the
reaction center (RC), a transmembrane enzyme, where they
generate a cascade of electron transfer reactions that results
in the double reduction
5
of the lipophylic mobile electron
carrier, ubiquinone-10. Following reduction the ubiquinone
takes up two protons from the cytoplasm, exits the RC and
migrates towards the ubiquinol–cytochrome c oxidoreduc-
tase (bc
1
), a second transmembrane complex. In the bc
1
complex the electrons are utilized to attract two more
protons and reduce the cytochrome c
2
, a water soluble
electron carrier that will eventually donate electrons to an
oxidized quinone sitting in the RC, thereby concluding the
cyclic electron transport driven by the solar radiation [8].

The net result of the entire photocycle is the light-sustained
translocation of a proton through the membrane, therefore
it is not surprising that a great effort has been made to
characterize the mechanism by which the excitons that are
absorbed by the RC, excite and shuttle electrons across the
enzyme. The large amounts of spectroscopic and structural
information that have been gathered have enabled a
relatively clear description of the electron transfer chain
reaction, which is initiated by the absorption of a photon or
an exciton. The excited electron is transferred from the
primary electron donor excited state D*(adimerof
bacteriochlorophyll a)
6
, to a chain of electron acceptors
located inside the protein at increasing distances from D [9].
Due to the spatial organization and the relative energies of
the cofactor redox couples, the forward electron transfer
reactions occur faster than the recombination reactions and
therefore, within hundreds of picoseconds, the electron
reaches the primary electron acceptor, ubiquinone-10, sitting
in the Q
A
7
pocket. In the absence of exogenous electron
donors (i.e. cytochrome) the charge separated state D
+
Q
A
–
has a lifetime

8
of 100 ms unless a loosely bound ubiquinone-
10 molecule is present in the
9
Q
B
pocket of the enzyme where
it acts as secondary electron acceptor. The state D
+
Q
B
–
is
more stable, with a lifetime of one or two seconds. In the
presence of cytochrome, the secondary quinone can allocate
a second electron yielded from the absorption of a new
photon, thereby functioning as a two-electron gate [3,10].
During transfer of the second electron from the primary to
the secondary quinone, protons reach the interior of the
protein [11]. Finally the quinol leaves the RC and is replaced
by the oxidized quinone sitting in the membrane pool [12].
Correspondence to M. Trotta, Istituto per i Processi Chimico-Fisici –
Sezione di Bari, Via Orabona 4-I 70126 BARI, Italy.
Fax: + 39 080 5442029, Tel.: + 39 080 5442027,
E-mail:
Abbreviations: bc
1
, ubiquinol-cytochrome c oxidoreductase; ICM,
intracytoplasmatic membranes; LDAO, lauryl dimethyl amino
N-oxide; LHC, light harvesting complex; RC, reaction center.

Dedication: Dedicated to the memory of Professor Mario Della
Monica.
(Received 18 September 2002, revised 12 September 2003,
accepted 22 September 2003)
Eur. J. Biochem. 270, 4595–4605 (2003) Ó FEBS 2003 doi:10.1046/j.1432-1033.2003.03845.x
Under saturating illumination, the photocycle time scale
is in the order of milliseconds. A key role in the photocycle is
played by the exchange of the two redox forms of the
quinone, between the protein interior and the bilayer. Some
considerations regarding the exchange reaction for the
oxidized quinone are made in this paper, based on
investigations into the charge recombination reactions that
take place in purified RCs reconstituted in proteoliposomes,
and in the absence of exogenous electron donors. Proteo-
liposomes were selected because they can be considered a
good mimicking system for the photosynthetic membrane,
in which the relative amounts of enzyme and quinone can
be altered easily, in contrast to the isolated ICM, called
chromatophores, where changing quinone concentration is
a laborious task [13]. Moreover, in the ICM the presence of
the entire and active electron transport chain would require
the use of decouplers in order to focus the RC–quinone
interaction. A final consideration for using liposomes is that
the solubilizing environment may play a role, particularly
when the Q
B
pocket is under investigation [14,15].
In this work, RCs were reconstituted in phosphatidyl-
choline liposomes, which are recognized for producing the
best results in the formation of small unilamellar vesicles.

The kinetics and equilibrium of the exchange between the
Q
B
pocket and the quinone pool were estimated. The
collected data were simulated with the well-known kinetic
scheme of Shinkarev & Wraight [16], and the kinetic
constants of the ligand uptake (k
in
)andrelease(k
out
)
processes were inferred. The single species time evolution
involved in the kinetic scheme was extracted from the
output of the numerical simulation. Recombination reac-
tions were also compared to different solubilizing environ-
ments such as reverse and direct micelles.
Materials and methods
Isolation of reaction centers and
Q
B
site depletion
Reaction centers were isolated from Rhodobacter sphaero-
ides strain R-26.1 following the procedure illustrated by
Isaacson et al. [17]. Protein purity was established using the
ratio of absorbance at 280 and 802 nm (A
280
/A
802
), which
was kept below 1.3, and the ratio of absorbance at 760 and

865 nm (A
760
/A
865
), which was equal to or lower than 1. The
average quinone content was 1.8 when defined by (Q/RC).
Depletion of the Q
B
site was accomplished using the
procedure of Okamura et al. [18], with the final prepara-
tions exhibiting a quinone content (Q/RC) ¼ 1.05 ± 0.05
as determined by the charge recombination decay. No
changes to the photobleaching amplitude were observed
upon addition of quinone.
Charge recombination kinetics were recorded at 865 nm
using a kinetic spectrophotometer implemented with an
Hamamatsu R928 photomultiplier (Hamamatsu Photo-
nics K.K., Hamamatsu City, Japan), and a Nd-Yag Laser
(Quanta System, Milan, Italy) which was used for RC
photoexcitation. Data were collected onto a Digital
Oscilloscope (Tektronix, Inc., TKS3052, Beaverton, OR,
USA) and trace deconvolution was performed using
software developed in-house. The decay traces were
recorded until complete recovery occurred following
photobleaching. Absorbance changes were measured
taking the baseline recorded before the flash as the
starting value. Even at high quinone concentrations, the
trace deconvolution was obtained with a high correlation
coefficient (r
2

) using bi-exponential functions. A drift of
less than 1.5% was observed in samples illuminated by the
sole measuring beam in the time range of the experiments.
Each point in the data shown below is the average of
three different liposome preparations.
Reaction center reconstitution in proteoliposomes
RC reconstitution in liposomes was accomplished following
the procedure outlined in [19–21]. One to eight milligrams of
1,2-diacyl-sn-glycero-3-phosphocholine (used at 48% pur-
ity, Sigma) were dissolved in 500 lL of chloroform to
which, when needed, aliquots of a 1 m
M
ubiquinone-10
(Sigma) solution were added. The resulting solution was
carefully dried under a stream of nitrogen in an Eppendorf
tube, to form an evenly distributed film of lipids. Five
hundred microlitres of a 4% (w/v) sodium cholate solution
(Sigma) in phosphate buffer, pH 6.8, 100 m
M
KCl were
added to the lipid film. Lipids were solubilized by 10–20
repeated one-second sonications (Sonifier Mod. 250, Bran-
son Ultrasonic Corporation, Danbury, CT, USA) to form a
homogenous solution. This solution was added to the
Q
B
site-depleted RC (90 l
M
), shaken vigorously and stored
for 15 min at 4 °C. Finally, the solution was loaded onto a

15 cm Sephadex G-50 Superfine column (Pharmacia)
previously equilibrated with the phosphate buffer. The
band containing RC incorporating liposomes elutes rapidly,
and optical measurements were carried out. Proteolipo-
somes were prepared with different quinone/RC (Q/RC)
ratios while still maintaining a constant enzyme concentra-
tion. The RC orientation in the liposome bilayer was
inferred from the decrease in the total amount of photo-
bleaching at 865 nm before and after the addition of
reduced cytochrome c (Sigma). The two possible orienta-
tions of RCs were found to be equally distributed.
Dynamic light scattering measurements. The hydro-
dynamic diameter of liposomes was determined by means of
dynamic light scattering using a Brookhaven Instruments
Corporation goniometer (BI-200SM) (New York, USA)
equipped with a helium/neon laser source (wavelength
632.8 nm). Samples were contained in cylindrical optical
cells with a diameter of 1 cm while an external thermostat
maintained the temperature at 20.0 ± 0.1 °C. All dynamic
light scattering determinations were made at a scattering
angle of 90°. Data were acquired within the 1–104 ns decay
time range that is necessary to determine the signal from
particles.
The diffusion coefficient D,
30
was extracted from the
measured autocorrelation function by a cumulants method
[22,23] using
BI
-

PCSW SIMPLE CUMULANTS
software (Brook-
haven Instruments Corporation, New York, USA).
In this method, the logarithm of the correlation function,
g(s),
31
fits to a power series of the correlation time (s):
ln gðsÞ
fg
¼ A þ Bs þ Cs
2
þ :::
where A is a constant that depends on the instrument
setting and
4596 F. Milano et al.(Eur. J. Biochem. 270) Ó FEBS 2003
B ¼À

C ¼ DQ
2
Q ¼ [4p · n · sen(Q/2)/k], with Q being the modulus of
the scattering vector, n being the refraction index of the
solution, k being the wavelength and Q/2 being the
scattering angle); and C is equal to
33
1
2
Z
1
0
ðC À


CÞ
2
CðCÞdC
2
4
3
5
where, C and C(C) are the decay velocity and the decay
velocity distribution, respectively). The ratio C/B
2
rep-
resents the size polydispersity distribution.
In the hypothesis that particles behave like hard spheres
the average hydrodynamic radius (R) was calculated from
D using the Stokes–Einstein equation,
R ¼ k
B
T=6pgD
where g is the water viscosity, k
B
is the Boltzmann
constant and T is the absolute temperature.
The geometry of the liposomes is in agreement with that
obtained by Palazzo et al. [24] for liposomes prepared in the
same way. Combining the parameters obtained for the
preparation of liposomes as summarized in Table 1, it is
possible to estimate a RC/liposome ratio of 500 ± 150
depending on the lipid/protein ratio used to prepare the
liposomes (see below). These values correspond to an RC

surface concentration ranging from 2.7 to 20.0 nmolÆm
2
.
The lower concentration is in agreement with 3.0 nmolÆm
2
calculated for chromatophores assigned a radius of 50 nm
[25,26] and using the 50–60 RC/chromatophore ratio as
found by Saphon et al.[27].
It is well known that the radius of liposomes is influenced
by the molar ratio of lipid/detergent in the mixed micelles
36
starting solution, and in our preparations this ratio was
always below the critical value of 1.33 at which the
transition between the extended bilayer sheet and the
micelle takes place. Each of the above described experiments
exhibits no significant variation in the diameter of the
liposomes with varying lipid/detergent molar ratio.
Due to dispersion of the data for the same sample we
conclude that an average value of 110 ± 25 nm can be
assumed as a reasonable
37
estimate of the liposomes radius.
The measurements made on both liposomes containing the
RC (proteoliposomes), and pure liposomes (not containing
protein), gave substantially the same results.
Reconstitution of the protein was confirmed by prepar-
ing liposomes in the presence of a fluorescent lipid
(1-palmitoyl-2-[12-[(7-nitro-2-1,3-benzoxadiazol-4-yl) amino]-
dodecanoyl]-sn-glycero-3-phosphocholine
38

purchased from
Avanti Polar Lipids Inc., Alabaster, AL, USA), and
recording the visible spectra and fluorescence of the solution
eluted from the column
39
[19]. The RC elutes in a single sharp
band that coincides with the lipid elution, indicating that the
proteins are completely reconstituted into liposomes.
40
Results and discussion
The kinetic scheme and data analysis
The reaction scheme outlined in Fig. 1 shows the kinetic
constants for the final electron acceptor reactions. The
reactions take place in the neutral state (lower row), and in
the charge separated state that is generated in the RC
following the absorption of a photon in the absence of an
exogenous electron donor (upper row). Several descriptions
of the scheme are available, the most detailed of which was
given by Shinkarev & Wraight [16].
In the dark the RCs undergo a binding equilibrium in
which the loosely bound quinones are taken up and released
from the Q
B
site [12]. After a short light pulse, the RCs
undergo a charge separation process, where an electron is
transferred from D to a primary quinone acceptor located in
the Q
A
binding site. For proteins in which the Q
B

pocket is
empty, a charge recombination occurs with a phenomen-
ological monoexponential decay constant [9] k
F
¼ k
AD
41
which is % 8s
)1
(k
F
is the phenomenological delay constant
of the fast phase and k
AD
is the back electron transfer
constant from the D
+
Q
A
–
and D
+
Q
A
–
Q
B
states). In RCs
which have the Q
B

pocket occupied, the electron rapidly
equilibrates between the two final acceptors with an equilib-
rium constant (L
AB
) that can be expressed as
42
L
AB
¼
k
AB
/k
BA
(k
AB
being the forward electron transfer constant
from D
+
Q
A
–
Q
B
to D
+
Q
A
Q
B
–

and k
BA
being the backward
electron transfer from D
+
Q
A
Q
B
–
to D
+
Q
A
)
Q
B
). When the
Q
B
pockets are fully occupied, the charge recombination
reaction is also monoexponential, with a phenomenological
rate constant, k
s
:
Table 1. Parameters of proteliposomes preparations. RC area assumes
a horizontal section as an ellipse [9] of 0.3 · 0.4 nm
2
. Liposome radius
derived from experimental data.

RC area
(nm
2
)
Liposome
radius (nm)
Liposome
area (nm
2
)
(Liposome
area/RC area)
10 110 ± 25 (1.5 ± 0.6) · 10
5
1.5 · 10
4
Fig. 1. The kinetic scheme for reaction centers in the presence of quinone
association and dissociation (quinone exchange), both in the dark and in
the charge separated state. Theconstantsintheschemearedefinedas
follows: k
AD
¼ back electron transfer constant from the D
+
Q
A
–
and
D
+
Q

A
–
Q
B
states, assuming that the charge recombination process from
Q
A
–
is not affected by the functional occupancy of the Q
B
site;
k
in
¼ quinone uptake constant; k
out
¼ quinone release kinetic con-
stant; k
AB
¼ forward electron transfer constant from D
+
Q
A
–
Q
B
to
D
+
Q
A

Q
B
–
; k
BA
¼ backward electron transfer from D
+
Q
A
Q
B
–
to
D
+
Q
A
–
Q
B
. The direct recombination route from D
+
Q
A
Q
B
–
is not
shown as its constant is negligible compared to the others. k
in

and k
out
are assumed to be independent of the redox state of Q
A
(see text for
discussion).
Ó FEBS 2003 Quinone exchange in liposomes (Eur. J. Biochem. 270) 4597
ðk
AD
þ k
BD
L
AB
Þ
1
1 þ L
AB

% k
AD
1
1 þ L
AB

Eqn ð1Þ
This approximation holds because the direct recombination
reaction from the D
+
Q
A

Q
B
–
state has a negligible kinetic
constant (k
BD
<0.1s
)1
) [28,29]. In the presence of a
subsaturating quinone concentration, only a fraction of the
Q
B
sites can be filled and the decay can be fitted with the
sum of two exponential decays:
DAðtÞ¼DA
0
fast
expðÀk
F
tÞþDA
0
slow
expðÀk
S
tÞ Eqn ð2Þ
where t is the time, DA(t) represents the amplitude at any
instant t,andDA
fast
0
and DA

slow
0
represent the amplitudes of
the fast and slow phase respectively.
Proteoliposomes were prepared using Q
B
depleted reac-
tion centers in the presence of increasing amounts of
ubiquinone-10,
45
the naturally occurring quinone in the Q
B
site. Charge recombination kinetics were recorded and time
evolution traces of absorbance changes were fitted
(r
2
> 0.995) using Eqn (2) where k
F
and k
S
represent the
phenomenological decay constants of the fast and slow
phase, respectively. In this work the k
F
constant is assumed
equivalent to the kinetic constant k
AD
(8.3 s
)1
) of the decay

from the Q
A
–
containing states (Fig. 1). Indeed, upon
addition of inhibitors of Q
B
functionality, the decay of the
charge separated state is monoexponential, with a constant
slightly faster than the k
F
(%10 s
)1
), indicating that the
secondary quinone is displaced from its binding site as
observed in detergent.
46
In contrast, k
S
results from more than one clear-cut
process as discussed below. As the quinone/RC ratio
47
increases, a rise
47; 48
in the slow phase amplitude and a decrease
in the decay constant are observed. Figure 2 shows the
dependence of the slow phase relative amplitude (titration
curve) on the increase of Q/RC. Similarly the dependence of
thedecayconstantisshowninFig.3.
Under these conditions the binding reaction has a role in
the slow component of the charge recombination. The slow

decay constant depends both on the rate ratio between the
quinone exchange and the charge recombination from the
states D
+
Q
A
–
or D
+
Q
A
–
Q
B
, in addition to Q/RC.
The quinone release rate k
out
[D
+
Q
A
)
Q
B
] can be normal-
ized to the back electron transfer rate from the appropriate
state; k
out
[D
+

Q
A
)
Q
B
]/k
AD
[D
+
Q
A
)
Q
B
], and the ratio can be
used to describe the quinone exchange regime. For instance,
if (k
out
/k
AD
) > 1 the exchange is defined as fast, whereas
for (k
out
/k
AD
) < 1 the exchange is defined as slow.
The different kinetic behaviour of the protein when
solubilized in different environments (e.g. direct micelles,
reverse micelles, and proteoliposomes) comes from the
influence played by the surroundings on k

in
, k
out
and L
AB
.
For instance, in direct lauryl dimethyl amino N-oxide
(LDAO)
49
micelles a decay sum of two exponential is
observed [18] with a subsaturating quinone concentration
[i.e. a fast phase with a decay constant (k
F
¼ k
AD
)anda
slow phase with a decay constant (k
S
) given by Eqn (1)],
that can be explained only by considering a slow exchange.
The quinone uptake and release can be neglected during the
charge recombination reaction, hence the relative amplitude
of the slow phase is proportional to the Q
B
site occupancy.
On the other hand, in direct Triton X-100 micelles a decay
sum of two exponentials is observed [30] with a subsaturat-
ing quinone concentration in which the k
S
depends on the

concentration of added quinone, ranging from 1.1 s
)1
to
2.7 s
)1
, showing a fast exchange at the Q
B
site. Agostiano
et al. [31] found that the charge separated state of RCs
solubilized in phospholipid reverse micelles will decay as the
sum of two exponentials. The reverse micelles are dissolved
in hexane where the unbound quinone is highly soluble. The
decay has a k
F
¼ k
AD
and a slow phase with a constant k
S
decreasing from 3 s
)1
to 1 s
)1
, and a relative amplitude
increasing to 1.0 for 400 £ Q/RC £ 7000. Such behaviour
was explained in terms of fast quinone exchange.
Assuming quinone molecules uniformly distributed
among vesicles of different sizes, Palazzo et al. [24] studied
the influence of the spread of the local solute concentration
on the phenomenological kinetic constants.
In the present work the Q/RC ratio ranged from 0.02 to

4, and full Q
B
reconstitution was obtained for values higher
than 3. The long chain exogenous quinone was confined to
Fig. 2. Fraction of slow phase obtained by fitting Eqn (1) to the
experimental traces. d, phosphatidylcholine proteoliposomes prepared
with lipid/protein molar ratio of 1000 : 1; [Q]/[RC], concentration of
the species in the mixed micelles, where [RC] ¼ 8.3 lM; s,2.1 l
M
RC
made up in 0.025% LDAO in 20 mM tris buffer pH 8, where the
quinone is solubilized in
64
Triton X-100.
Fig. 3. Slow phase decay constant as a function of quinone/RC molar
ratio. d, liposomes; s,detergent.
4598 F. Milano et al.(Eur. J. Biochem. 270) Ó FEBS 2003
the liposome bilayers. Additionally, as a direct consequence
of our liposome preparation method, a solute molecule
distribution weighted by the bilayer vesicle volume was
considered (i.e. larger vesicles will contain larger numbers of
solute molecules). As shown in the Appendix, under this
assumption the average local volume concentration of
quinones is the same for aggregates of all sizes and the
polydispersity can be neglected at high overall quinone
concentration [Q]. In the investigated [Q] concentration
range this condition is not fulfilled for the first two values,
where the decay from the D
+
Q

A
–
state is predominant.
Analogously to the previous case, the decay of the charge
separated state is fitted by the sum of two exponentials with
k
F
¼ k
AD
and a slow phase k
S
decreasing from 1.5 s
)1
to
0.5 s
)1
. Using the asymptotic k
S
value in the equilibrium
constant, L
AB
is found to be 15.6. It should be noted that
when the condition (k
out
/k
AD
) > 1 occurs, the quinone
uptake and release take place during the charge recombi-
nation reaction. The exchange regime and the value of some
constants for the three solubilizing environments are

summarized in Table 2.
Numerical simulations
The set of differential equations [Eqn (3)] required for the
kinetic scheme shown in Fig. 1 was numerically solved by a
fourth order Runge–Kutta method. Using this approach a
value for the quinone uptake and release kinetic constants
and therefore the quinone binding constant (K
B
¼ k
in
/k
out
)
can be determined. The symbols used in Eqn. (3) are the
same as those used in [16]. Numerical simulations have been
carried out for the lipid/protein molar ratio 1000 : 1 by
using the values listed in Table 3.
dx/dt ¼Àðk
AD
þ k
in
qÞx þ k
out
y
dy/dt ¼ k
in
qx þ k
BA
z Àðk
AD

þ k
AB
þ k
out
Þy
dw/dt ¼ k
out
u þ k
AD
x À k
in
qw
dz/dt ¼ k
AB
y Àðk
BA
þ k
BD
Þz
du/dt ¼k
in
qw þ k
AD
y þ k
BD
z À k
out
u
dq/dt ¼Àk
in

qqðw þ xÞþk
in
ðy þ uÞq
8
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
:
Eqn ð3Þ
where x ¼½D
þ
Q
À
A

=½RC; y ¼½D
þ
Q
À
A
Q
B
=½RC; z ¼
½D
þ
Q
A
Q
À
B
=½RC; w ¼½DQ
A
=½RC; u ¼½DQ
A
Q
B
=½RC;
q ¼½Q
free
=½Q
total
and q ¼½RC=½Q
total
.
Immediately after the flash, at time zero, the electron is

found only in the charge separated states involving the
primary electron acceptor, i.e. D
+
Q
A
and D
+
Q
A
–
Q
B
, while
Q
B
has not yet been reached. The D
+
Q
A
–
Q
B
state rapidly
disappears, with constant k
AB
generating the state
D
+
Q
A

Q
B
–
, until the equilibrium is attained within few
milliseconds. Simultaneously, the charge separated states
start to decay and the different contributions cannot be
resolved by monitoring the D
+
decay. The free quinone
concentration ([Q]
free
) drops from its equilibrium ÔdarkÕ
value and is driven to the Q
B
site by the presence of the
electron. A typical time-evolution obtained by solving
Eqn(3)isshowninFig.4.
The quinone binding constant K
B
was varied in the range
1 · 10
5
) 1 · 10
7
M
)1
and the quinone release constant
k
out
was varied between 0.25 and 2500 s

)1
, spanning from a
slow to a fast exchange regime; this is shown in Fig. 5
where the charged species decay is simulated for seven k
out
values at constant K
B
. The slow decay constant k
s
is weakly
dependent on k
out
for large and small k
out
/k
AD
values,
whereas the dependence increases when this ratio is close
to 1. The overall dependencies of simulated k
s
and DA
0
slow
upon K
B
and k
out
/k
AD
are illustrated in Fig. 6.

The k
in
and k
out
values that minimize the square-root
difference between the simulated and experimental traces
were obtained by using the Ôsimple search methodÕ [32] with
a tolerance of 10
)4
giving k
in
¼ 7.2 · 10
7
M
)1
Æs
)1
and
k
out
¼ 40 s
)1
. From the best fit values, K
B
¼ 1.8 · 10
6
M
)1
and k
out

/k
AD
¼ 4.8 were obtained.
The agreement between the experimental and the simu-
lated data for the reconstitution of Q
B
site experiments in
proteoliposomes (Fig. 7) is very satisfying.
Discussion
An important issue arising from the above experimental
and simulated data is the different behaviour of the
quinone exchange when passing from direct micelles to
Table 2. Constants and exchange domains for three different solubilizing environments.
RC solubilizing environment k
AD
(s
)1
) L
AB
K
B
(
M
)1
) k
out
/k
AD
LDAO direct micelles 8.3 9–10
a

10
7
<1
LDAO direct micelles [51] 8.3 20 10
7
<1
Triton X-100 direct micelles [30] 8.3 % 6–8
a
% 5 · 10
7
>1
Phospholipids reverse micelles 8.3 11.5 1.2 · 10
4
>1
Phosphatidylcholine proteliposomes
b
8.3 15 1.8 · 10
6
4.8
65
a
Calculated from the equation (k
AD
/k
S
) ) 1 using the values k
AD
¼ 8.3 s
)1
and k

s
¼ 0.8 s
)1
[16].
b
This work.
Table 3. Numerical value for the constants employed in the simulation of
D
+
decay. L
AB
is taken from Table 2; k
AB
and k
BD
from [28] [29]; k
BA
is obtained from the assumption that the forward electron transfer
constant in proteoliposomes remains unaltered. Recently, Taly et al.
[52] measured, with 10% uncertainty, k
AB
¼ 8700 s
)1
for the wild type
(Rb. sphaeroides 2.4.1) in dimyristoylphosphatidylcholine liposomes.
The numerical simulation has also been tested for different k
AB
values
and it was found to be insensitive for rates in the range
5000 s

)1
) 15000 s
)1
.
Constant Value
k
AB
10
4
s
)1
k
BD
1 · 10
)2
s
)1
k
BA
6.6 · 10
2
s
)1
66
k
AD
8.3 s
)1
Ó FEBS 2003 Quinone exchange in liposomes (Eur. J. Biochem. 270) 4599
proteoliposomes. The main difference between these two

solubilizing environments is their organization with the
enzyme. RC–LDAO complexes have been characterized by
small angle neutron scattering [33,34]. The complex is
formed by a toroidally shaped group of micelles surround-
ing the most hydrophobic part of the protein. In these
complexes the detergent around the protein is organized
with the chain perpendicular to the protein surface and with
the terminal region sticking into the protein. This reduces
the hydrophobic portion of the detergent in which free
quinone can diffuse (% 1500 A
˚
3
) [33]. Crystallographic data
[14] shows that the detergent itself is located in the channel
into which the quinone isoprenoid chain sits in the enzyme.
This explains the slow exchange process of the quinone at its
binding site. Conversely, the dimensions of Triton X-100
micelles [35] are larger than those formed by LDAO,
thereby allowing a larger quinone pool size as well as higher
ligand mobility.
The proteoliposomes are topologically similar to the
detergent–RC
50
complexes, i.e. they are disconnected solubi-
lizing environments, but they differ because proteolipo-
somes can allocate a large number of proteins, in the order
of hundreds of RCs per vesicle. As a consequence, the
number of quinones per liposome ranges from tens to
hundreds, and fluctuations in the local concentration can be
neglected. Liposomes can therefore be used for drawing

general conclusions on quinone binding at the Q
B
site. The
lipophylic environment represented by proteoliposomes has
several advantages in describing the exchange of quinone in
photosynthetic membranes compared to the RC–detergent
complexes: (a) the quinone is arranged in the bilayer in a
similar manner to chromatophores, where quinone can
freely diffuse towards and away from the enzyme, and the
large volume of the bilayer allows the accommodation a
large number of ligands; (b) the arrangement of the lipid
molecules around the RC is not known, but it can be
reliably assumed that they will not attach with their chains
into the protein. No direct interaction with the Q
B
site is
expected and the channel will always be accessible for the
quinone exchange; (c) The absolute value of k
s
measured in
detergent is larger than the one obtained in saturating
conditions in liposomes, indicating a relative stabilization of
Q

À
B
. This difference in the semiquinone stability might be
associated with small detrimental changes in the Q
B
pocket,

induced by the detergent hydrophobic chains that are absent
in the case of liposomes. The absence of detrimental effects
in liposomes is also confirmed by the D

þ
electron nuclear
double resonance spectra as recently reported by our group
[19].
Some considerations on the absolute value of the quinone
exchange constants in proteoliposomes can be useful in
order to understand the same process in photosynthetic
membranes. For a bimolecular reaction of an enzyme with a
small ligand, a reasonable approximation of the frequency
Fig. 4. Numerical simulation of time evolution
following light pulses of D
+
Q
A
–
, D
+
Q
A
–
Q
B
,
D
+
Q

A
Q
B
–
and D
+
Q
free
. Q/RC ¼ 0.74;
[RC] ¼ 8.3 l
M
; K
B
¼ 10
6
M
)1
; k
out
¼ 25. The
initial ten milliseconds of the time-course are
shownintheinsert.
Fig. 5. Simulated decay of D
+
obtained for Q/RC = 0.37 and a
binding constant of K
B
=10
6
M

)1
. Different decays were obtained
with different k
out
. The noisy line represents the recorded trace in
the experimental conditions used for the simulation.
4600 F. Milano et al.(Eur. J. Biochem. 270) Ó FEBS 2003
of collision (f
C
) in the diffusion controlled regime can be
obtained by simple considerations on the mobility of the
two species [36]:
f
C
¼ 4pr
0
ðD
RC
þ D
Q
ÞÁ10
À3
N
A
% 4pr
0
D
Q
Á 10
À3

N
A
Eqn ð4Þ
r
0
is the minimum approaching distance in cm, assumed
to be equal to the radius of the protein; N
A
is the
Avogadro Number; D
RC
and D
Q
represent the diffusion
coefficients of the RC and quinone, respectively. The
approximation in Eqn (4) is based on the large difference
in the dimension of the colliding molecules. For mito-
chondrial cytochrome bc
1
, a diffusion constant D ¼ 4.0 ·
10
)11
cm
2
Æs
)1
was measured [37,38] and a similar order of
magnitude can be expected for the RC, as both are large
membrane proteins.
Several techniques have been used to measure the

ubiquinone-10 diffusion coefficient D
Q
. Using fluorescent
quenching [39–42] the diffusion coefficient was found to
span the range 1 · 10
)7
) 5 · 10
)6
cm
2
Æs
)1
.Withthe
fluorescent recovery after photobleaching technique, a value
in the range 1 · 10
)8
) 5 · 10
)8
cm
2
Æs
)1
was obtained
[37,43,44]. Electrochemical methods were also used, and a
value of (2.0 ± 0.4) · 10
)8
cm
2
Æs
)1

was obtained [45].
According to Blackwell and coworkers [41,42] the D
Q
obtained using the fluorescence quenching method can be
disregarded because it overestimates the actual value.
Therefore, using D
Q
¼ 2.0 · 10
)8
cm
2
Æs
)1
in Eqn (4), an
f
C
value equal to 5.0 · 10
7
M
)1
Æs
)1
is obtained. It should be
noted that although the collision frequency is slightly
overestimated because Eqn (4) is valid for three-dimen-
sional systems, this value remains within the accuracy of
these considerations.
Assuming the surface of the Q
B
channel entrance to be

the area of the protein where a successful collision can take
place [46], an estimate of the association constant can be
made. Assuming % 30 A
˚
2
and 5000 A
˚
2
for the quinone
moiety, and L and M subunit surfaces in contact with the
lipids respectively, a correction factor of 0.006 is obtained.
As a consequence k
in
can be estimated to be 3 · 10
5
M
)1
Æs
)1
which is very close to the result of the best-fit procedure
(k
in
¼ 7.2 · 10
7
), corrected by the factor [L]v¢
tail
(see
Appendix) giving k
in
[L]v¢

tail
¼ 3.6 · 10
5
M
)1
Æs
)1
. This sug-
gests that the rate limiting step for the association of the RC
Fig. 6. Three dimensional representation of (A) k
s
and (B) DA
0
slow
dependence on K
B
and k
out
/k
AD
. For k
out
/k
AD
< 1 (slow exchange), the fraction of
slow phase coincides with the fraction of occupied Q
B
sites in the dark adapted state. The k
s
obtained under such conditions is independent, as

expected, of the concentration of quinone in the solubilizing environment, matching the value from Eqn (1). For k
out
/k
AD
> 1 (fast exchange), the
fraction of slow phase does not coincide with, and moreover, over-estimates the fraction of Q
B
sites occupied in the dark adapted state.
Fig. 7. Comparison between simulated (s) and experimental values (d)
for k
s
(A) and DA
0
slow
(B) as functions of Q/RC.
Ó FEBS 2003 Quinone exchange in liposomes (Eur. J. Biochem. 270) 4601
and quinone is the diffusion of the latter through the
proteoliposomes, implying that the ligand in the binding
channel, either taken up or released, moves at least as fast as
in the bilayer; this can be expressed as (D
Q
)
channel
‡ D
Q
.
Assuming a random transfer for quinone, it will cover the
binding channel of length

X (% 50 A

˚
) in an average time of
(1/k
diff
) £ (

X
2
/2D
Q
) % 2 · 10
)5
s.
The average time for quinone release, obtained from the
simulations of 1/k
out
¼ 25 ms, accounts for both the
residence time in the channel (1/k
diff
)andforthetime
required to unbind from the pocket (1/k
P
):
1
k
out
¼
1
k
diff

þ
1
k
P
%
1
k
P
¼ 25 ms Eqn ð5Þ
As a consequence, the bottleneck in the quinone release
process is represented by the unbinding of the ligand from
its pocket. The value of 25 ms obtained from Eqn (5), is
comparable with that of %2 ms obtained by NMR
measurements for systems kept in the dark in the presence
of ubiquinone-10 [47]. The results differ by one order of
magnitude, and the discrepancy can be attributed to the
assumption that the charge separated and neutral RCs
exchange quinones with the same kinetics, regardless of the
redox state of Q
A
(Fig. 1), as we assume that the presence of
the hydrophobic tail has no influence on k
P
. This suggests
that in the charge separated state the quinone release is
slower than in the dark. This can be explained by invoking
the gated propeller twist imposed on Q
B
by the presence of a
negative charge on Q

A
[48] that buries the quinone head in
the inner part of the Q
B
pocket, thereby increasing the
interaction energy between the ligand and the binding site.
In a forthcoming work the exchange kinetic dependence on
the Q
A
redox state will be addressed.
The results obtained in this paper can be related to the
RC photocycle, when the photochemistry takes place in the
presence of an exogenous electron donor able to doubly
reduce D
+
. Gerencser et al. [49] have measured the steady-
state rate of cytochrome c turnover in detergent, demon-
strating that at low ionic strength the reaction of
cytochrome c
3+
unbinding from the RC is the rate limiting
step of the photocycle (1000 s
)1
< k
off
< 2000 s
)1
). By
employing the simulated k
in

¼ 7.2 · 10
7
M
)1
Æs
)1
value, it is
possible to estimate the [Q]
min
at which quinone uptake
is not the rate limiting step: k
in
· [Q]
min
> 1000 s
)1
Þ
[Q]
min
>14lm, which agrees with the value of 25 l
M
used
in Gerencser’s work. Such [Q]
min
can easily be obtained
in our preparation and would give a quinone pool of
Q/RC % 3, which is smaller than the average dimension of
the quinone pool in chromatophores [50].
Interestingly the structure of the Q
B

pocket and the
quinone in the illuminated crystals [48] shows a strong
interaction between the protein residues and the quinoid
moiety of the ligand, based on the formation of hydrogen
bonds. These bonds will, of course, disappear following
the double reduction of the RC photocycle and protona-
tion of the quinone; in some way driving the release of the
quinol. It is quite tempting to conclude that the release of
the quinol from the binding pocket would be faster than
the quinone release because of the weaker interaction
between the Q
B
pocket and the reduced ligand. Presently
however, the results only permit the setting of a lower
limit on the release rate of quinol, which will lead to a
resultlargerthanthesameratefortheoxidizedform:
53
(k
out
)
QH
2
‡ (k
out
)
Q
. Conversely, from the hypothesis that
cytochrome turnover would be unchanged in both the
vesicle and in detergent, i.e. that the unbinding of oxidized
cytochrome would remain the slowest step of the photo-

cycle, the upper limit for the quinol release can be set to
(k
out
)
QH
2
£ 1000 s
)1
.
Conclusions
By studying the charge recombination kinetics of reaction
centers incorporated into liposomes, thermodynamic and
kinetic parameters have been inferred which regulate the
photosynthetic turnover of this important protein. These
values, although obtained in a simpler environment, can be
reasonably taken as a fair approximation to the ones
actually working in the natural ICMs.
The high value found for the quinone equilibrium binding
constant K
B
¼ (k
in
/k
out
) ¼ 1.8 · 10
6
M
)1
, makes it possible
for the reaction centers to efficiently work with a small

quinone pool: we found that with a quinone/protein molar
ratio as small as three, the Q
B
site was fully occupied. When
the electron reaches the Q
A
site in a reaction center without
the quinone in the Q
B
pocket, only the charge recombina-
tion reaction can occur, which results in a loss of excitation
energy. However, in physiological conditions, where the
quinone pool size has been estimated to be 10 or larger, this
is very unlikely to happen. It would be interesting to
investigate similar reconstituted systems prepared with
RC mutants with smaller charge recombination rate
(k
AD
) constants which fulfil the slow exchange regime in
liposomes.
54
Acknowledgements
The authors are grateful to Professor E. Caponnetti and Dr Lucia
Pedone of Dipartimento di Chimica Fisica – Universita
´
di Palermo for
performing the dynamic light scattering measurements. Thanks also to
La
´
szlo

´
Nagy and Pe
´
ter Maro
´
ti for helpful discussions. This work was
made possible thanks to the financial support of the Grants:
Meccanismi Molecolari della Fotosintesi (FIRB-MIUR) and Cofin –
MIUR 2002.
References
1. Collins, M.L.P. & Remsen, C.C. (1991) The purple phototrophic
bacteria. In Structure of Phototrophic Prokaryotes (Stolz, J.F.,
ed.), pp. 49–77. CRC Press, Boca Raton, FL, USA.
2. Oelze, J. & Drews, G. (1972) Membranes of photosynthetic bac-
teria. Biochim. Biophys. Acta 265, 209–239.
3. Verme
´
glio, A., Joliot, P. & Joliot, A. (1995) Organization of
electron transfer components and supercomplexes. In Anoxygenic
Photosynthetic Bacteria (Blankenship, R.E., Madigan, T.M. &
Bauer, C.E., eds), pp. 279–295. Kluwer Academic Publisher,
Dordrecht, Boston, London.
4. Zuber, H. & Cogdell, R.J. (1995) Structure and organization of
purple bacterial reaction antennae complexes. In Anoxygenic
Photosynthetic Bacteria (Blankenship, R.E., Madigan, T.M. &
Bauer, C.E., eds), pp. 315–348. Kluwer Academic Publisher,
Dordrecht, Boston, London.
5. Gromet-Elhanan, Z
55
. (1995) The proton-translocating F

0
F
1
ATP
synthase–ATPase complex. In Anoxygenic Photosynthetic Bacteria
52
4602 F. Milano et al.(Eur. J. Biochem. 270) Ó FEBS 2003
(Blankenship, R.E., Madigan, T.M., & Bauer, C.E., eds),
pp. 807–820. Kluwer Academic Publisher, Dordrecht, Boston,
London.
6. Freiberg, A. (1995) Coupling of antennaes to reaction centers. In
Anoxygenic Photosynthetic Bacteria (Blankenship, R.E., Madigan,
T.M., & Bauer, C.E., eds), pp. 385–398. Kluwer Academic Pub-
lisher, Dordrecht, Boston, London.
7. Mauzerall, D.C. & Greenbaum, N.L. (1989) The absolute size of a
photosynthetic unit. Biochim. Biophys. Acta 974, 119–140.
8. de Grooth, B.G., van Grondelle, R., Romijn, J.C. & Pulles, M.P.
(1978) The mechanism of reduction of the ubiquinone pool in
photosynthetic bacteria at different redox potentials. Biochim.
Biophys. Acta 503, 480–490.
9. Feher, G., Allen, J.P., Okamura, M.Y. & Rees, D.C. (1989)
Structure and function of bacterial photosynthetic reaction cen-
tres. Nature 339, 111–116.
10. Wraight, C.A. (1977) Electron acceptors of photosynthetic bac-
terial reaction centers. Direct observation of oscillatory behaviour
suggesting two closely equivalent ubiquinones. Biochim. Biophys.
Acta 459, 525–531.
11. Okamura, M.Y. & Feher, G. (1995) Proton-coupled electron
transfer reactions of QB in reaction centers from photosynthetic
bacteria. In Anoxygenic Photosynthetic Bacteria (Blankenship,

R.E., Madigan, T.M. & Bauer, C.E., eds), pp. 577–594. Kluwer
Academic Publisher, Dordrecht, Boston, London.
12. McPherson, P.H., Okamura, M.Y. & Feher, G. (1990) Electron
transfer from the reaction centres of Rb. sphaeroides to the qui-
none pool: doubly reduced Q
B
leaves the reaction centres. Biochim.
Biophys. Acta 1016, 289–292.
13. Venturoli, G., Fernandez-Velasco, J.G., Crofts, A.R. & Melandri,
B.A. (1986) Demonstration of a collisional interaction of ubiqui-
nol with the ubiquinol-cytochrome c2 oxidoreductase complex in
chromatophores from Rhodobacter sphaeroides. Biochim. Biophys.
Acta 851, 340–352.
14. Lancaster, C.R. & Michel, H. (1997) The coupling of light-induced
electron transfer and proton uptake as derived from crystal
structures of reaction centres from Rhodopseudomonas viridis
modified at the binding site of the secondary quinine, QB. Struc-
ture 5, 1339–1359.
15. Nagy, L., Fodor, E., Farkas, T., Gedey, S. & Kecskes, A. (1998)
Lipids effect the charge stabilisation in wild type and mutant
reaction centres of photosynthetic bacteria Rhodobacter sphaer-
oides.InPhotosynthesis: Mechanisms and Effects.
56
Proceedings of
the 11th International Congress on Photosynthesis (Garab, G., ed.),
pp. 893–896. Kluwer Academic Publishers, Dordrecht, the Nether-
lands.
16. Shinkarev, V.P. & Wraight, C.A. (1993) Electron and proton
transfer in the acceptor quinone complex of reaction centres of
phototrophic bacteria. In The Photosynthetic Reaction Center

(Deisenhofer, J. & Norris, J.R., eds), pp. 193–255. Academic Press,
San Diego, CA, USA.
17. Isaacson,R.A.,Lendzian,F.,Abresch,E.C.,Lubitz,W.&Feher,
G. (1995) Electronic structure of Q-A in reaction centers from
Rhodobacter sphaeroides. I. Electron paramagnetic resonance in
single crystals. Biophys. J. 69, 311–322.
18. Okamura, M.Y., Isaacson, R.A. & Feher, G. (1975) The primary
acceptor in bacterial photosynthesis: the obligatory role of ubi-
quinone in photoactive reaction centres of Rp. Sphaeroides. Proc.
NatlAcad.Sci.USA72, 3491–3495.
19.Trotta,M.,Milano,F.,Nagy,L.&Agostiano,A.(2002)
Response of membrane protein to the environment: the case of
photosynthetic reaction centre. Material Science and Engineering:
C 22, 263–267.
20. Venturoli, G., Trotta, M., Feick, R., Melandri, B.A. & Zannoni,
D. (1991) Temperature dependence of charge recombination from
the P
+
QA
–
and P
+
QB
–
states in photosynthetic reaction centres
isolated from thermophilic bacterium Chloroflexus aurantiacus.
Eur. J. Biochem. 202, 625–634.
21. Kutuzov, M.A., Mamedov, M.D., Semenov, A.Yu., Shinkarev,
V.P., Verkhovsky, M.I., Abdulaev, N.G., Drachev, L.A. (1991)
Functioning of quinone acceptors in the reaction center of the

green photosynthetic bacterium Chloroflexus aurantiacus. FEBS
Lett. 289, 179–182.
22. Ford, N.C. Jr (1985)
58
Light Scattering Apparatus. In Dynamic
Light Scattering, Applications of Photon Correlation Spectroscopy
(Pecora, R., ed), pp. 7–34. Plenum Press, New York, NY, USA.
23. Schurtenberger, P. & Hauser, H. (1984) Characterisation of the
size distribution of unilamellar vesicles by gel filtration, quasi-
elastic light scattering and electron microscopy. Biochim. Biophys.
59
Acta 778, 470–480.
24. Palazzo, G., Mallardi, A., Giustini, M., Berti, D. & Venturoli, G.
(2000) Cumulant analysis of charge recombination kinetics in
bacterial reaction centres reconstituted in liposomes. Biophys. J.
79, 1171–1179.
25. Drews, G. & Golecki, J.R. (1995) Structure, molecular organisa-
tion, and biosynthesis of membranes of purple bacteria. In
Anoxygenic Photosynthetic Bacteria (Blankenship, R.E., Madigan,
T.M., & Bauer, C.E., eds), pp. 231–257. Kluwer Academic Pub-
lisher, Dordrecht, Boston, London.
26. Golecki, J.R. & Oelze, J. (1980) Differences in the architecture of
cytoplasmic and intracytoplasmic membranes of three chemo-
trophically and phototrophically grown species of the Rhodos-
pirillaceae. J. Bacteriol. 144, 781–788.
27. Saphon, S., Jackson, J.B., Lerbs, V. & Witt, H.T. (1975) The
functional unit of electrical events and phosphorylation in chro-
matophores from Rhodopseudomonas sphaeroides. Biochim. Bio-
phys. Acta 408, 58–66.
28. Kleinfeld, D., Okamura, M.Y. & Feher, G. (1984) Electron

transfer in reaction centres of Rhodopseudomonas sphaeroides.I.
Determination of the charge recombination pathway of D
+
Q
A
Q
–
B
and free energy and kinetic relations between Q
–
A
Q
B
and Q
A
Q
–
B
.
Biochim. Biophys. Acta 766, 126–140.
29. Paddock, M.L., Graige, M.S., Feher, G. & Okamura, M.Y. (1999)
Identification of the proton pathway in bacterial reaction centers:
inhibition of proton transfer by binding of Zn
2+
Cd
2+
. Proc. Natl
Acad. Sci. USA 96, 6183–6188.
30. Wraight, C.A. & Stein, R.R. (1983) Bacterial reaction center as a
model for PSII. Turnover of the secondary acceptor quinone.

In Oxygen Evolving System of Photosynthesis (Inoue, Y., Crofts,
A.R., Govindjee, Murata, N., Renger, G. & Satoh, K., eds), pp.
383–392. Academic Press, Tokyo, Japan
60
.
31. Agostiano, A., Catucci, L., Colafemmina, G., Della Monica, M.,
Palazzo, G., Giustini, M. & Mallardi, A. (1995) Charge recom-
bination of photosynthetic reaction centres in different membrane
models. Gazz. Chim. Ital. 125, 615–622.
32. Lagarias, J.C., Reeds, J.A., Wright, M.H. & Wright, P.E. (1998)
Convergence properties of the Nelder-Mead simplex method in
low dimensions. SIAM J. Optimization 9, 112–147.
33. Roth, M., Lewitt-Bentley, A., Michel, H., Deisenhofer, J.,
Huber, R. & Oesterhelt, D. (1989) Detergent structure in crystals
of a bacterial photosynthetic reaction centre. Nature 340, 656–662.
34. Roth, M., Arnoux, B., Ducruix, A. & Reiss-Husson, F. (1991)
Structure of the detergent phase and protein–detergent inter-
actions in crystals of the wild-type (strain Y) Rhodobacter sph-
aeroides. Biochemistry 30, 9403–9413.
35. Gast, P., Hemelrijk, P.W., Van Gorkom, H.J. & Hoff, A.J. (1996)
The association of different detergents with the photosynthetic
reaction centre protein from Rhodobacter sphaeroides R26 and the
effects on its photochemistry. Eur. J. Biochem. 239, 805–809.
36. Cantor, C.R. & Schimmel, P.R. (1980). Biophysical Chemistry:
Techniques for the Study of Biological Structure and Function.
61
WH
Freeman&Co.,SanFrancisco,CA,USA
62
.

Ó FEBS 2003 Quinone exchange in liposomes (Eur. J. Biochem. 270) 4603
37. Gupte, S., Wu, E.S., Hoechli, L., Hoechli, M., Jacobson, K.,
Sowers, A.E. & Hackenbrock, C.R. (1984) Relationship between
lateral diffusion, collision frequency, and electron transfer of
mitochondrial inner membrane oxidation-reduction components,
Proc.NatlAcad.Sci.USA81, 2606–2610.
38. Hackenbrock, C.R., Gupte, S., Wu, E.S. & Jacobson, K. (1984)
Lateral diffusion, collision and efficiency of oxidation-reduction
components in mitochondrial electron transport. Biochem. Soc.
Trans. 12, 402–403.
39. Fato, R., Battino, M., Degli-Esposti, M., Parenti-Castelli, G. &
Lenaz, G. (1986) Determination of partition and lateral diffusion
coefficients of ubiquinones by fluorescence quenching of
N-(9-anthroyloxy) stearic acids in phospholipid vesicles and
mitochondrial membranes. Biochemistry 25, 3378–3390.
40. Lenaz, G., Samorı
`
, B., Fato, R., Battino, M., Parenti-Castelli, G.
& Domini, I. (1992) Localization and preferred orientations of
ubiquinone homologs in model bilayers. Biochem. Cell Biol. 70,
504–514.
41. Blackwell, M.F. & Whitmarsh, J. (1990) Effect of integral
membrane proteins on the lateral mobility of plastoquinone
of phosphatidylcholine proteoliposomes. Biophys. J. 58, 1259–
1271.
42. Blackwell, M.F., Gounaris, K., Zara, S.J. & Barber, J. (1987) A
method for estimating lateral diffusion coefficients in membranes
from steady-state fluorescence quenching studies. Biophys. J. 51,
735–744.
43. Rajarathnam, K., Hochman, J., Schindler, M. & Ferguson-Miller,

S. (1989) Synthesis, location, and lateral mobility of fluorescently
labeled ubiquinone 10 in mitochondrial and artificial membranes.
Biochemistry 28, 3166–3176.
44. Chazotte, B. & Hackenbrock, C.R. (1991) Lateral diffusion of
redox components in the mitochondrial inner membrane is
unaffected by inner membrane folding and matrix density. J. Biol.
Chem. 266, 5973–5979.
45. Marchal,D.,Boireau,W.,Laval,J.M.,Moiroux,J.&Bourdillon,
C. (1998) Electrochemical measurement of lateral diffusion coef-
ficients of ubiquinones and plastoquinones of various isoprenoid
chain lengths incorporated in model bilayers. Biophys. J. 74,
1937–1948.
46. Agostiano, A., Milano, F. & Trotta, M. (1999) Investigation on
the detergent role in the function of secondary quinone in bacterial
Reaction Centers. Eur. J. Biochem. 262, 358–364.
47. Trotta, M., Feher, G. & Okamura, M.Y. (1992) NMR studies of
quinone binding to reaction centres from Rb. Phaeroides. Biophys.
J. 61, A101
63
.
48. Stowell, M.H., McPhillips, T.M., Rees, D.C., Soltis, S.M.,
Abresch, E.C. & Feher, G. (1997) Light-induced structural chan-
ges in photosynthetic reaction center: implications for mechanism
of electron-proton transfer. Science 276, 812–816.
49. Gerencser, L., Laczko, G. & Maroti, P. (1999) Unbinding of
oxidized cytochrome c from photosynthetic reaction center of
Rhodobacter sphaeroides is the bottleneck of fast turnover. Bio-
chemistry 38, 16866–16875.
50. Hauska, G. & Hurt, E. (1982) Pool function behaviour and
mobility of isoprenoid quinones. In Function of Quinones in Energy

Conserving Systems (Trumpower, B.L., ed), pp. 87–110. Academic
Press, New York, NY, USA.
51. Shinkarev, V.P. & Wraight, C.A. (1997) The interaction of qui-
none and detergent with reaction centres of purple bacteria. I.
Slow quinone exchange between reaction centre micelles and pure
detergent micelles. Biophys. J. 72, 2304–2319.
52. Taly, A., Baciou, L. & Sebban, P. (2002) The DMPC lipid phase
transition influences differently the first and the second electron
transfer reactions in bacterial reaction centers. FEBS Lett. 532,
91–96.
Appendix
In this section the distribution of a highly hydrophobic solute
among vesicles of different sizes will be addressed, assuming
vesicles to be spherical compartments with bi-layered
boundaries of negligible thickness. Moreover, the existence
of a density probability function P(R) should also be defined
as follows: P(R) dR equals the probability to find a V
R
vesicle
with radius between R and R + dR. At this level of
approximation, the overall concentration of vesicles [V]can
be calculated in terms of the lipid concentration [L]bythe
surface area conservation law per unit volume:
½La ¼½V
Z
8pR
2
PðRÞdR ¼½V8phR
2
i Eqn ð6Þ

a being the lipid head area. Additionally, the bilayer
volume can be also estimated according to Palazzo et al.
[24], as the product of the lipid number on the vesicle
bilayer surface (8pR
2
/a) multiplied by the lipid tail
volume v
tail
:
mðRÞ¼ð8pR
2
=aÞÂm
tail
Eqn ð7Þ
The distribution of solute molecules S, among spherical
vesicles V, of different radius R, can be then described with
the following density function:
Pðn; RÞ¼PðnjRÞPðRÞ Eqn ð8Þ
where P(n, R) dR is the probability to find n solute molecules
inside a V
R
vesicle (i.e. an aggregate of size between R and
R + dR), and it equals the products of the probability
P(R) dR to find a V
R
vesicle multiplied by the conditional
probability P(n|R) to find n solute molecules in this
aggregate.
As a consequence of Eqn (8) the average number of
solute molecules ÆNæ among vesicles of any size is obtained

by the summation over all possible solute molecule numbers
and the integration over all vesicle size ranges:
hNi¼
Z
X
n
nPðnj RÞPðRÞdR ¼
Z
hNðRÞiPðRÞdR
Eqn ð9Þ
As shown by the previous equation, ÆNæ can also be
expressed in terms of the average numbers of solute
molecules among V
R
compartments: ÆN(R)æ ¼
S
n
nP(n|R). The term ÆN(R)æ can also estimate, in terms
of macroscopic concentration, the ratio between the
bulk concentration of S molecules contained in V
R
vesicles ([S
R
]), divided by the bulk concentration of these
aggregates [V
R
]:
hNðRÞi ¼
½S
R


½V
R

Eqn ð10Þ
[V
R
] is directly linked to the overall vesicle bulk
concentration [V] by the equation [V
R
] ¼ [V]P(R) dR,
whereas different hypotheses can be found on the
relationship between [S
R
] and [S], depending on the
experimental preparation method. Herein two main
assumptions will be considered: (a) the solute molecule
distribution is independent of the vesicle radius, (b) the
4604 F. Milano et al.(Eur. J. Biochem. 270) Ó FEBS 2003
solute molecule distribution is weighted on the volume
of the vesicle bilayer v(R).
If a random distribution is assumed among vesicles, i.e.
no dependence on the size is considered, then
[S
R
] ¼ [S]P(R)dR so that by using Eqns (10 and 6) one
obtains:
hNðRÞi ¼
½S
½V


¼
½S
½L

8phR
2
i
a

Eqn ð11Þ
therefore ÆN(R)æ is independent of the specific vesicle radius
R. It will however, depend on the second moment of the
P(R) probability density function: ÆR
2
æ ¼ ÆRæ
2
+ r
2
.In
fact, at fixed [L] if the average size of vesicles increases then
their overall concentration [V] must decrease and ÆN(R)æ
must increase. On the other hand, in the case of the bilayer
volume weighted distribution, the concentration [S
R
] will
result:
½S
R
¼½S

mðRÞPðRÞdR
R
mðRÞPðRÞdR

¼½S
R
2
hR
2
i

ðPðRÞdRÞ
and by means of Eqns (10 and 6) the average number of
solute molecules in R sized vesicles will be:
hNðRÞi ¼
½S
½L

8pR
2
a

Eqn ð12Þ
in this case ÆN(R)æ is proportional to the bilayer vesicle
volume.
Defining the solute vesicle volume concentration as the
mole number of solute molecules in a vesicle divided by the
bilayer volume: (S
R
)

V
¼ n/(N
A
v(R)), we can now calculate
the average Æ(S)
V
æ:
hðSÞ
V
i¼

Z
X
n
n
N
A
vðRÞ

ðPðnjRÞPðRÞdRÞ
¼
Z
hNðRÞi
N
A
vðRÞ

ðPðRÞdRÞ
N
A

being the Avogadro number.
In scenario (a), by using Eqns (11, 6 and 7) one obtains:
hðSÞ
V
i¼
½S
½L
1
v
0
tail

ðhR
2
iÞ
Z
PðRÞdR
R
2

%
½S
½L
1
v
0
tail

hR
2

i
hRi
2
!
Eqn ð13Þ
where v¢
tail
¼ v
tail
N
A
, as obtained by Palazzo et al. [24].
On the other hand, in scenario (b) ÆN(R)æ can be
calculated using Eqns (12, 6 and 7):
hNðRÞi ¼
½S
½V

R
2
hRi
2
!
¼
½S
½L

8pR
2
a


Eqn ð14Þ
and the average solute concentration will result:
hðSÞVi¼
½S
½L

1
m
0
tail

Eqn ð15Þ
The previous equation clearly shows that in the case of a
solute distribution weighted on the bilayer volume, the
average vesicle volume concentration of solute Æ(S)
V
æ is
independent of the vesicle size, and the experimental results
from different vesicle size distributions can be directly
compared. Moreover, at fixed lipid concentration [L], Æ(S)
V
æ
is proportional to the bulk solute concentration [S]andthis
allows one to use this value in the kinetic equations, keeping
in mind that the bimolecular kinetic constants used in
Eqn (8) must be corrected multiplied by [L]v¢
tail
to obtain
the real constants.

Another important point is to estimate the standard
deviation of Æ(S)
V
æ and this can be done by first calculating:
hðSÞ
2
V
i¼
Z
X
n
n
N
A
mðRÞ

2
!
ÂðPðnjRÞPðRÞdRÞ ¼ ðhðSÞ
V
i
2
Þ
þ
½S
½L

a
8pm
02

tail

1
R
2

and then obtaining the polydispersity index:
P
hSi
¼

hS
2
i
hSi
2

À 1 ¼
½L
½S

a
8p

1
R
2

%
½L

½S

a
8p

1
hR
2
i

whilst keeping in mind Eqn (15). P
ÆSæ
shows that by
increasing the bulk solute concentration or the average
radius of liposomes, the (S) polydispersity decreases.
In the studied case the RC concentration gives:
[RC]
molÆL
)1
Æ(RC)
V
æ
molÆL
)1
r
Æ(RC)æ
molÆL
)1
P
Æ(RC)æ

67
8.3 · 10
)6
1.5 · 10
)3
7.1 · 10
)5
2.2 · 10
)3
whereas for the quinone we obtain:
[Q]
total
molÆL
)1
Æ(Q)
V
æ
molÆL
)1
r
Æ(Q)æ
molÆL
)1
P
Æ(Q)æ
1.5 · 10
)7
2.7 · 10
)5
9.5 · 10

)6
1.2 · 10
)1
3.1 · 10
)5
5.6 · 10
)3
1.3 · 10
)4
5.9 · 10
)4
showing that only at very low concentration of
quinones, the spread of the concentration distribution
becomes not negligible.
Ó FEBS 2003 Quinone exchange in liposomes (Eur. J. Biochem. 270) 4605