Semiquinone oscillations as tool for investigating the ubiquinone binding to
photosynthetic reaction centers.
Supplementary material
Fulvio Ciriaco#, Rocco Roberto Tangorra#, Alessandra Antonucci#, Livia Giotta†, Angela Agostiano
§,#
, Massimo Trotta§, Francesco Milano§.
§ Italian National Research Council, Institute for Physical and Chemical Processes (CNR-IPCF),
70126 Bari, Italy,
# Department of Chemistry, University of Bari, 70126 Bari, Italy,
† Department of Biological and Environmental Sciences and Technologies (DiSTeBA), University
of Salento, 73100 Lecce, Italy
Optimization algorithm, best fit parameters reliability and their mutual interactions.
The program, written in C language and provided in a separate file, provides both a simple
optimization algorithm and some data analysis capabilities. The key steps of the optimization are
shown in figure S1.
Figure S1. Summary of the three key steps implemented in the C-code used to simulate and fit the
oscillation patterns, namely parameters initialization, dark relaxations and light reactions.
The fitness function is a sum over each single flash of (me-ms)2+(de-ds)2, where m is the mean
absorbance in the interval between two subsequent flashes and d the absorbance difference in the
same interval; the subscript e and s refer to experimental and simulated respectively.
The optimization algorithm in the provided code is a simple pattern search golden section type. This
is not very efficient for a large number of parameters but the very short time required for each
single experiment simulation makes it acceptable.
The program may also be used as a plugin for external optimization methods. A stripped version
that uses only standard input and outputs has also been written for this specific purpose. Both BFGS
(Fletcher, 1970) and CMA-ES (Igel, 2007) were tested.
CMA-ES is an evolutionary optimizer that deduces from the sampling also first and second
derivative information for guiding the subsequent population generation. Depending on initial
hessian and on population size it can explore a much larger portion of the parameter landscape than
local optimizers.
BFGS is very efficient, as could be deduced from the plausible double differentiability of the fitness
function. Also, as a by-product, it provides a quite good inverse hessian at the minimum.
A method to assert the reciprocal interaction of the fitting parameters is the analysis of the
eigenvalues and eigenvectors of the hessian. There are four main contraindications against this
approach:
• it requires a rather strict minimization of σ2, small deviations from the minimum can affect the
most interesting hessian eigenvectors and even introduce negative eigenvalues;
• it does not work for parameters that have attained an extremal value, e.g. for a parameter x
constrained in the interval [0,1] that has a fitting value of 1;
• it requires a thorough analysis of all the eigenvectors, which can be a daunting effort for a large
set of parameters. One can however analyse only the eigenvectors associated to the smallest
eigenvalues if a suitable metric for the parameter displacements is established;
• it is based on second derivatives and affords only a local view of σ dependence on parameter
values.
A quite common misconception about optimization, probably derived by polynomial interpolation
is that a function with n parameters will always fit an n point curve.
This is plainly wrong, unless the fitting function is carefully crafted, like in the polynomial
interpolation example.
In general, “blindingly” adding parameters can bring small or no advantage to the fitness.
For example, one might be tempted to introduce an oxidation constant for each of the species Q A Q B
and Q A Q B , however since the concentration of the two species are proportional one to another it is
not really possible to physically distinguish the two processes on the 0.01s timescale.
The two parameters would be collinear in this case and one could be eliminated straightforwardly
without any impact on the rest of the simulation (except for a general improvement of the
convergence properties of the optimizer).
In figure S2 isovalue lines of the fitness are plotted as a function of selected parameters of physical
interest.
Figure S2. Plot of error correlation for selected parameters.
In a strict neighborhood of the optimal value, the curves are ellipses with axes dictated by the
hessian matrix. However, the lines can have different shapes away from the center; the locality of
the hessian analysis is in fact its main limit. The longer axis (provided the plot metric is uniform) is
the region where the parameters can deviate more from the optimal value without significantly
affecting the fitness. When the curve axes are parallel to the cartesian axes, the parameters are
orthogonal and have well distinct meanings to the physics of the problem.
In the first plot of figure S2 for example, KQ and KE are not orthogonal, they mostly can deviate
from the optimal value along a line that is approximately KQ∙KE = const. This happens because what
the flashes effectively measure is the concentration of Q A Q B that in the limit of small Q∙KQ is in
fact proportional to KQ∙KE. The plot also shows the confidence interval for KQ according to the
classical definition (the smaller segment) and how the interval is extended due to the correlation
with KE (the larger segment). The values reported in the second column of table S1, denoted
“extended confidence interval”, refer in fact to the extremal values of each parameter on the surface
of constant χ2 displaced from its minimum value by 1·σ2, hence taking into account the
simultaneous variation of all other parameters. The confidence interval is instead reported in the
first column of table S1 together with the best fit values.
In conclusion, analysis of the eigenvectors of the hessian matrix bound to the lowest eigenvalues
and of the correlation plots not only establish the limits within which the obtained values of the
parameters are statistically bound but also provide more insight into the complicated shape of the
fitting function and the significance of the introduced parameters.
Table S1. Best fit values of oscillation parameters for the UQ10 case and assessment of errors.
Oscillation pattern
KQ,bulk
(5.8±0.5) ∙105 M–1
Oscillation pattern
extended confidence intervals
(3.2‒11.7) ∙105 M–1
KQ,det
175±15 M–1
106‒388 M–1
KE
6.2±0.3
4.9‒8.4
fl_eff
0.98
0.98
ml_eff
0.030
0.030
kSA
(15±2) ∙103 M-1s-1
(9‒32) ∙103 M-1s-1
kSB
(5.0±0.3) ∙103 M-1s-1
(3‒14) ∙103 M-1s-1
kQH
(17±2) ∙103 M-1s-1
(11‒73) ∙103 M-1s-1
Determination of quinone binding constant to the QB site of RC for UQ0 in 0.025% LDAO and UQ10
in 0.03% Triton X-100.
For the KQ determination with the alternate method exploiting the charge recombination reaction
(CRR), we make use of the new weighted amplitude (WA) method introduced in (Mavelli et al.
2014). QB-depleted RC where added with increasing amounts of quinone, and the relevant charge
recombination reactions were recorded at 865 nm. Each trace was fitted to a biexponential function,
from which two main phases are obtained, namely a fast phase, having fractional amplitude AF and
recombination time τF , and a slow phase having amplitude fractional AS and recombination time τS.
Both AS and τS increase with the amount of added quinone; in particular AS increases from 0 to 1
and τS increases up to its maximum value τ∞ when the QB-site is fully occupied. By plotting the
quantity AS∙τS/τ∞ (the wighted amplitude) as a function of added quinone and by fitting the data to a
quadratic function, the binding constant of quinone to RC can be inferred. This method is not
influenced by the kinetic characteristic of the binding quinone.
The results for the UQ0 titration in LDAO are shown in figure S3A, along with the fitting curve
bringing about KQ = 2.05∙103 M–1; figure S3B shows the results for UQ10 in Triton X-100, with KQ
= 6.8∙105 M–1.
B
A
Figure S3. QB-site titration in QB-depleted RC solved in Tris 15 mM, EDTA 1 mM, LDAO 0.025%
(panel A) and Tris 15 mM, EDTA 1 mM, TX 0.03% (panel B) at pH 8. [RC] = 1 µM. In panel A,
UQ0 was added from a 40 mM aqueous stock solution, while in panel B UQ10 was added from a
600 µM stock solution containing TX 0.3%.
Study of the quinol reoxidation reaction.
Quinol reoxidation was studied by following the pH variations upon proton uptake and release due
to the quinone redox reactions:
RC,hν
+

 UQ10H 2 +2fcnMeOH +
UQ10 +2H +2fcnMeOH 

As is well known, quinol reduction occurs in two steps and is accompanied by a sub-stoichiometric
proton uptake after the first flash, and is completed by the overall uptake of two protons after the
second flash. Due to its low redox potential, the UQ10H2 species is then reoxidized with parallel
proton release in the solution. These reactions were followed in low buffering capacity conditions
using the spectrophotometric pH indicator cresol red at pH around 8, at 572 nm.
The kinetics of quinol reoxidation was followed in conditions similar to that used for the
oscillations (see figure S4). The signal decay after one or more pair of flashes was interpolated
either by a monoexponential function, suitable for pseudo-first order reactions, or by the following
function, suitable for bimolecular reactions:
A  t  =A +
CA0exp  CkQH t 
C  A0  exp  CkQH t   1
where kQH is the rate constant of the bimolecular reaction, (expressed in A–1s–1), A0 is the
absorbance at t = 0, A∞ is the absorbance at t = ∞ and C is the initial concentration difference
between the two reagents, measured in terms of absorbance.
By sending to the system more flash pairs, it is possible to study the effect of the reagents initial
concentration increase, which eases the distinction between a first or a second order reaction.
Figure S4. Decay kinetics of UQ10H2 recorded after 2,4,6,8 and 12 flashes followed through the
optical response of pH indicator dye cresol red. Conditions: RC 2 µM, UQ10 20 µM, TX 0.03%,
KCl 100 mM, FcnMeOH 300 μM, cresol red 20 µM, pH ~8.0.
It is possible to observe that pH reaches a plateau after 8 flashes, indicating a balance between
ubiquinol production and consumption. Reoxidation rates clearly increase with the number of
flashes. In the following table, the values of the parameters for the mono- or bimolecular fitting are
reported together with the relevant r2.
Flash n.
kQH
mono r2
(s–1)
kQH
A0
C
r2
(A–1s–1)
2
0.164
0.995
5.26
0.0287
0.0186
0.9997
4
0.209
0.994
4.64
0.0453
0.0263
0.9999
6
0.230
0.993
4.54
0.0518
0.0294
0.9991
8
0.264
0.995
4.59
0.0516
0.0363
0.9995
12
0.290
0.995
5.04
0.0501
0.0358
0.9997
All kinetic traces could be approximately interpolated by the monoexponential function (r2 > 0.993
for all traces, but rate constant increases sensibly with the flash number. The traces are indeed much
better interpolated using the bimolecular function (r2 > 0.9991) and, more importantly, the relevant
kinetic constant is almost independent on the flash number.
It is useful to convert the bimolecular rate constant from absorbance units to concentration: after
two flashes we measured ΔA = 0.029 corresponding to the production of one mole of ubiquinol per
RC, i.e [UQ10H2] = 2 μM, hence the apparent Δε is 14500 M–1cm–1. The bimolecular rate constant is
therefore 7.0∙104 M–1s–1.
Fitting of the reoxidation traces indicates that the ubiquinol is reoxidized by the FcnMeOH+
produced by the flash light plus certain amount of another reagent that is pre-existent, but not in
large excess as indicated by the value of the parameter C which is always roughly half with respect
to A0. The most obvious species could be a certain amount of FcnMeOH+ existing before the
flashes as result of the redox equilibrium between FcnMeOH and its oxidized counterpart. Indeed
the ubiquinol reoxidation rate at different solution redox potentials adjusted by addition of
ferrocyanide was found to decrease as the potential was lowered (data not shown). This indicates
that the concentration of one of the oxidizing agents, either the photoproduced FcnMeOH+ or other
species preexisting to the flashes, decreased with decreasing of the potential. Direct observation of
FcnMeOH+, followed at 629 nm (where a peak of FcnMeOH+ is present and the semiquinone
spectra are flat) as shown if figure S5 enables to confirm that this is the pre-existing oxidizing
species. In fact, in the absence of ferrocyanide, a series of upward steps are observed, corresponding
to the formation of FcnMeOH+. If the same experiment is repeated in the presence of ferrocyanide 1
mM the obtained trace is flat indicating that this species rapidly re-reduces the FcnMeOH+ before
its reaction with ubiquinol, which results stabilized by the lacking of its oxidizing species.
Figure S5. Time evolution of a solution containing RC 2 μM, UQ10 40 μM, FcnMeOH 300 μM in
Tris 15 mM, EDTA 1 mM, TX 0.03% pH 8 exposed to 7 equispaced flashes at 10 Hz, measured at
629 nm (black trace). Grey trace was recorded in the presence of ferrocyanide 1 mM.
Ubiquinol reoxidation was finally observed directly at 294 nm after 2 and 8 flashes as shown in
figure S6.
Figure S6. Time evolution of a solution containing [RC] 2 μM, [UQ10] 40 μM, [FcnMeOH] 300
μM in Tris 15 mM, EDTA 1 mM, TX 0.03% pH 8 exposed to 8 equispaced flashes at 10 Hz,
measured at 294 nm (black circles). Data were fitted according to either a first (dashed line) or a
second order (continuous line) mechanism.
The results are summarized in the following table, using again as interpolating function again the
mono- or the bimolecular one.
Flash n.
k mono (s–1)
r2
2
0.037
8
0.064
k (A–1s–1)
A0
C
r2
0.993 -
-
-
-
0.993 2.45
0.04
0.004
0.999
For the absorbance to molarity conversion, we used the initial amplitude of the signal after two
flashes corresponding to the generation of [UQ10H2] = 2 μM. From the observed ΔA value of 0.013,
Δε = 6500 M-1cm-1 could be calculated. The value kQH = 2.45 A–1s–1 was hence converted to kQH =
2.1∙104 M–1s–1 which is in in good agreement with and previous measurements at 249 nm where
disappearance of ferrocenium was followed (Milano et al. 2007) and in excellent agreement the
value found by the oscillation pattern.
Fitting of oscillation traces recorded at 770 nm.
Even though the oscillation recorded at 770 nm are not perfectly suitable for extracting quantitative
parameters for the reasons explained in the main text, the data fitting has been performed for the
traces collected with Q/RC =3 and in the presence or absence of ferrocyanide 10 mM.
Both traces are fitted with good approximation using the proposed model, in fair agreement with the
results found at 450 and 395 nm. As expected, the only difference is the optimized parameters is in
the KQH, which is zero in the presence of ferrocyanide, and 1.6∙105 M-1s- if ferrocyanide is omitted.
with FeCy
without FeCy
KQ,bulk
1.5∙106 M–1
1.5∙106 M–1
KQ,det
211 M–1
175 M–1
KE
7.4
7.4
fl_eff
1
1
ml_eff
0.03
0.03
kSA
1.0∙104 M-1s-1
1.0∙104 M-1s-1
kSB
7.0∙105 M-1s-1
7.0∙105 M-1s-1
kQH
0
1.6∙105 M-1s-1
15
Absorbance • 1000
+ 10 mM ferrocyanide
10
5
0
-2
0
2
4
6
8
10
12
consecutive flashes
Figure S7. Semiquinone oscillations recorded at 770 nm, in the presence (grey trace) or in the
absence (black trace) of Ferrocyanide 10 mM. Red and green traces are the relevant fittings
respectively. Conditions: [RC] = 1 µM, [UQ10] = 3 µM, FcnMeOH 300 µM, flash repetition rate =
1 Hz, buffer T10E1TX0.03 pH 8.0.
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