Photosynth Res
DOI 10.1007/s11120-013-9894-2
REGULAR PAPER
A model of chlorophyll a fluorescence induction kinetics
with explicit description of structural constraints of individual
photosystem II units
Chang-Peng Xin • Jin Yang • Xin-Guang Zhu
Received: 27 February 2013 / Accepted: 11 July 2013
Springer Science+Business Media Dordrecht 2013
Abstract Chlorophyll a fluorescence induction (FI) kinetics, in the microseconds to the second range, reflects the
overall performance of the photosynthetic apparatus. In this
paper, we have developed a novel FI model, using a rule-based
kinetic Monte Carlo method, which incorporates not only
structural and kinetic information on PSII, but also a simplified photosystem I. This model has allowed us to successfully
simulate the FI under normal or different treatment conditions,
i.e., with different levels of measuring light, under
3-(30 ,40 -dichlorophenyl)-1,1-dimethylurea treatment, under
2,5-dibromo-3-methyl-6-isopropyl-p-benzoquinone
treatment, and under methyl viologen treatment. Further, using this
model, we have systematically studied the mechanistic basis
and factors influencing the FI kinetics. The results of our
simulations suggest that (1) the J step is caused by the twoThis manuscript is written in honor of Professor Govindjee for his
monumental contributions to photosynthesis research and education.
Electronic supplementary material The online version of this
article (doi:10.1007/s11120-013-9894-2) contains supplementary
material, which is available to authorized users.
C.-P. Xin J. Yang X.-G. Zhu (&)
CAS Key Laboratory of Computational Biology, CAS-MPG
(Chinese Academy of Sciences-German Max Planck Society)
Partner Institute for Computational Biology, Shanghai Institutes
for Biological Sciences, Chinese Academy of Sciences,
Shanghai 200031, China
e-mail: zhuxinguang@picb.ac.cn
C.-P. Xin X.-G. Zhu
State Key Laboratory of Hybrid Rice Research, Changsha
410125, Hunan, China
C.-P. Xin X.-G. Zhu
Shanghai Institute of Plant Physiology and Ecology, Shanghai
Institute of Biological Sciences, Chinese Academy of Sciences,
Shanghai 200032, China
electron gate at the QB site; (2) the I step is caused by the rate
limitation of the plastoquinol re-oxidation in the plastoquinone pool. This new model provides a framework for
exploring impacts of modifying not only kinetic but also
structural parameters on the FI kinetics.
Keywords Chlorophyll fluorescence induction Kinetic model Photosynthesis Rule-based kinetic
Monte Carlo methods Systems biology
Abbreviations
Cytb6f
Cytochrome b6f complex
DBMIB 2,5-Dibromo-3-methyl-6-isopropyl-pbenzoquinone
DCMU 3-(30 ,40 -Dichlorophenyl)-1,1-dimethylurea
ETC
Electron transfer chain
Fd
Ferredoxin
FNR
Ferredoxin–NADP reductase
FI
Fluorescence induction
FM
Maximum chlorophyll fluorescence
F0
Minimum chlorophyll fluorescence
F(t)
Fluorescence at time t
MV
Methyl viologen
OEC
Oxygen evolving complex
P680
Primary electron donor in photosystem II
PC
Plastocyanin
Pheo
Pheophytin—primary electron acceptor in
photosystem II
PQ
Plastoquinone
PSI
Photosystem I
PSII
Photosystem II
QA
The first quinone electron acceptor in
photosystem II
QB
The second quinone electron acceptor in
photosystem II
123
Photosynth Res
RCII
V(t)
YZ
Reaction center of photosystem II
Relative variable fluorescence (= (F(t) - F0)/
(FM - F0))
Tyrosine 161—secondary electron donor
located in D1 protein of photosystem II
Introduction
In higher plants, de-excitation of the excited state of the
chlorophyll molecules of the antenna of photosystem II
(PSII) occurs through three major pathways: primary photochemistry after excitation energy transfer to reaction
centers, dissipation as heat, and emission as light (fluorescence) (Govindjee et al. 1986; Govindjee 1995, 2004; Stirbet and Govindjee 2011). As a consequence, chlorophyll
a fluorescence yield is influenced by the proportion of light
energy used by the other two processes; therefore, measuring chlorophyll fluorescence can provide information about
the amount of light energy used in photochemistry and heat
dissipation (Maxwell and Johnson 2000; Papageorgiou and
Govindjee 2011). Thus, chlorophyll a fluorescence is used
as a signature of photosynthesis; further, it has been shown
to play an important role in our current efforts to develop
screening for phenomics (Govindjee 1995; Furbank et al.
2009). One of the commonly used tool is to measure chlorophyll fluorescence induction (FI) curves (the Kautsky
effect) using high light intensities; in the current terminology, it is the OJIP chlorophyll a FI curve, which describes
the process of fluorescence increase from an initial low level
O (or F0) to a maximum level P (or FM) through two
intermediate steps, termed J and I, or FJ and FI (Strasser
et al. 1995; Strasser et al. 2004; Stirbet and Govindjee 2011).
Chlorophyll a FI kinetics reflects the overall performance of
the photosynthetic apparatus (Govindjee 1995; Strasser
et al. 1995; Papageorgiou and Govindjee 2004; Strasser
et al. 2004; Zhu et al. 2005; Lazár 2006; Lazár and Schansker 2009; Stirbet and Govindjee 2011). The improved
knowledge of molecular mechanisms underlying the O, J, I,
and the P steps will therefore facilitate the application of FI
kinetics in large-scale screening studies.
There have been many attempts to study the mechanistic
basis of FI curve in the past (Lazár 2006; Lazár and Schansker
2009; Rubin and Riznichenko 2009; Schansker et al. 2013).
Due to the difficulty of directly measuring the redox changes
of the electron transfer chain (ETC) components in vivo,
some of these studies have used as a modeling approach and
gained substantial insights regarding the mechanisms of FI
kinetics. Some of these models are based on a subset of
reactions around PSII. Three basic models have been used in
fast FI simulation: (1) the two-electron gate (TEG) model
which describes the electron transport between the first
123
quinone electron acceptor QA and the second quinone electron acceptor QB, and taking into account the fact that QB can
accept two electrons (Crofts and Wraight 1983; BougesBocquet 1973; Velthuys and Amesz 1974); (2) the reversible
radical pair (RRP) model which describes excitation energy
transfer, primary charge separation, charge recombination,
and charge stabilization taking place at the PSII reaction
center level (Breton 1983; Van Grondelle 1985; Schatz et al.
1988; Leibl et al. 1989; Roelofs et al. 1992; Lavergne and
Trissl 1995); and (3) the Kok model (Kok et al. 1970) which
describes the function of the donor side of PSII, i.e., the S state
cycle of the oxygen evolving complex (OEC). Baake and
Schlöder (1992) combined the TEG model with the RRP
model and fitted FI curves measured at low light intensities.
Then, Stirbet et al. (1998) combined the TEG model with the
Kok model to simulate the FI kinetics under high light
intensity. Then, Lebedeva et al. (2002) developed a model to
simulate the FI over a range of light intensities which combined the TEG model with the RRP model. In the model
proposed by Lebedeva et al. (2002), the effect of electric
membrane potentials on the rate constants of several reactions, including Q2B protonation, QBH2/plastoquinone (PQ)
exchange, and P680? reduction, were incorporated. However,
the models proposed by Baake and Schlöder (1992) and Lebedeva et al. (2002) did not include the molecular mechanism
of the OEC (i.e., the Kok model, also called the oxygen
clock). On the other hand, the models of Lazár (2003) and Zhu
et al. (2005) were a combination of TEG, RRP, and Kok
models and they provided a detailed description of the reactions around PSII to simulate the fast FI curve. However,
these two models (Lazár 2003; Zhu et al. 2005) still included a
number of assumptions that are incompatible with biological
reality. For example, Lazár (2003) and Zhu et al. (2005)
described the QBH2/PQ exchange by a second-order kinetic
reaction and considered the OEC ‘‘virtually’’ separated from
PSII (Lazár and Jablonský 2009). However, the QBH2/PQ
exchange is better described by two subsequent reactions and
the OEC being considered bound to PSII (Lazár and Jablonský 2009). Some of the models (see e.g., Zhu et al. 2005)
have ignored that the reactions within a PSII electron transport chain are restricted to the same complex.
To explore the potential impacts of the spatial arrangement of different components on FI, Lazár and Jablonský
(2009) developed a FI model in which the OEC was bound
to PSII, the QBH2/PQ exchange was described by two
subsequent reactions, and all the electron transport reactions were restricted to the same complex. This study
showed that different structural and kinetic rules can lead
to qualitatively different results (Lazár and Jablonský
2009). Although, it is feasible to use ordinary differential
equations (ODE) to simulate a system with a limited and
small number of components, developing a complex model
describing detailed spatial arrangement (constraints) using
Photosynth Res
ODE-based modeling approach quickly becomes intractable. This is because with an increase in the model complexity, it becomes practically impossible to enumerate all
the intermediate states of the photosynthetic system. Since
the goal of the work by Lazár and Jablonský (2009) was to
study the effects of different approaches on the FI curve,
the model that was used had been highly simplified, e.g.,
tyrosine Z (or Yz), which is between the OEC and P680, and
pheophytin (Pheo), which is between P680 and QA were not
included.
In addition, most of the previous models (e.g., Lazár
et al. 1997; Stirbet et al. 1998; Lazár 2003; Zhu et al. 2005)
considered only the electron transport reactions occurring
from the reaction center of PSII to the PQ pool. However,
experimental studies suggest that photosystem I (PSI) plays
a significant role in the FI kinetics, especially during the
I–P phase (Munday and Govindjee 1969; Schansker et al.
2003, 2005). Results from previous models (Lazár et al.
1997; Stirbet et al. 1998; Lazár 2003; Zhu et al. 2005) have
shown that considering PSII alone is not sufficient to
simulate experimental FI curves. Lazár (2009) extended the
model of Lazár and Jablonský (2009) to include both the
PSI pigment protein complex and the electron transport
components around PSI (i.e., Cyt b6f and FNR, ferredoxin–
NADP reductase), and studied the effects of PSI electron
transfer reactions on FI. And the results have shown that
the electron transport reactions occurring beyond PSII
affect the shape of the FLR (Lazár 2009).
In this paper, we use the Monte Carlo method, which
has been used earlier in photosynthesis research (Lavorel
and Joliot 1972; Lavorel 1973, 1986; Antal et al. 2013). A
specific development of a rule-based kinetic Monte Carlo
(KMC) method (Yang et al. 2008), which was originally
designed to simulate signal transduction processes in
multi-site protein complexes, offers a solution to tackle
the complexity of enumerating all the intermediate states
of the chlorophyll protein complexes that are related to
the FI kinetics. Here, we have used this approach to
simulate the FI kinetics. Compared to the earlier models
of the FI curve, this new approach has the following
features: (1) the stochasticity of reactions is explicitly
described; (2) the light capture, excitation energy transfer,
and electron transfer associated with PSII on both the
donor and the acceptor sides are described in detail; (3)
the structural relationship between different components
in the photosystem is preserved, e.g., the reactions within
PSII electron transport are restricted to the same complex,
e.g., each OEC is only linked to one PSII unit; (4) PSII
units are organized into groups, the excitation energy is
assumed to only migrate from closed reaction centers to
open reaction centers in the same group; and (5) all the
electron transfer reactions beyond PQ pool were simplified by assuming one PSI electron acceptor pool that can
accept a finite number of electrons. We have shown that
this FI model provides a framework to study the relationship between FI kinetics and different structural and
biochemical properties of PSII. We have simulated the FI
kinetics under normal conditions and under different
treatments, i.e., 3-(3,4-dichlorophenyl)-1,1-dimethylurea
(DCMU) treatment; 2,5-dibromo-3-methyl-6-isopropyl-pbenzoquinone (DBMIB) treatment; and methyl viologen
(MV) treatment. Also, this model has allowed us to study
the mechanisms underlying FI kinetics and the effects of
changes in the rate constants of the donor side of PSII on
FI kinetics. Further, we have analyzed the effects of
different PSII group sizes on the FI curve.
Materials and methods
The model structure and assumptions
As shown in Scheme 1, our model is composed of the
following major components: antenna system of PSII,
OEC, P680, Pheo, the redox-active Tyrosine of D1 protein,
QA, QB, the PQ pool, and the PSI acceptor pool. Here, we
list the reactions and assumptions used in this model (see
Scheme 1 for a diagram of the current model). Most of
these assumptions are similar to those in Zhu et al. (2005)
and others (reviewed in Lazár and Schansker 2009):
(1)
(2)
(3)
The formation of the excited state of chlorophyll is
described by a chlorophyll excitation rate constant
KL. KL is the number of photons received per
chlorophyll per second, which is proportional to the
excitation light intensity (Baake and Schlöder 1992;
Lazár 1999, 2003; Lazár and Jablonský 2009; Lazár
2009).
De-excitation of the excited state of Chl occurs
through three major pathways, i.e., (a) primary photochemistry that leads to charge separation in the
reaction center, P680*Pheo, directly, or after transfer
of excitation energy from closed to open reaction
centers; (b) non-radiative loss of the excitation energy
(i.e., heat dissipation) in the antenna and in the
reaction center; and (c) Chl a fluorescence emission.
The primary photochemistry (i.e., the charge separation, recombination, and stabilization, i.e., transfer
of electrons from Pheo- to QA) is described
according to the RRP model (Leibl et al. 1989;
Roelofs et al. 1992; Lavergne and Trissl 1995; Lazár
2003; Zhu et al. 2005). The charge recombination
reaction (radiationless) between P680? and QA
(Haveman and Mathis 1976; Renger and Wolff
1976) is also included in this model.
123
Photosynth Res
a
b
PSII group
PSII group
PSII group
PSII group
PSII group
PSII group
Excited
Energy
PSIIO
PSIIC
e-
c
S1
S0
S2
S4
O2 +4H+
e-
Antenna
(Yz)
Heat
Light
P680
Pheo
*
P680
Pheo
+
P680
Pheo
P680
Pheo
2H2O
e
e-
P680
Pheo
-
S3
Oxygen Evolving Complex
+
P680
Pheo
Fluorescence
and Heat
QAQB
QA-QB
QAQB-
QA-QB-
QAQB2-
QA-QB2-
PQH2
QAΕ
QA-
PSI acceptor
pool
PQ
PQ pool
PQ
Scheme 1 Diagram of the current chlorophyll a fluorescence induction model. a Energetically connected PSII units are organized into
groups. b The excitation energy transfer from a closed reaction center
(PSII_C) to an open reaction center (PSII_O) can take place only in
the same PSII group. c A block flow diagram of the electron and
energy transport in a QB-reducing PSII unit. All reactions are
described by rules detailed in Table 3 in ‘‘Appendix’’. The section
enclosed by the dotted line in (c) represents the charge separation and
(4)
The electron transfer from the reduced QA to QB is
described with a TEG model (Bouges-Bocquet 1973;
Velthuys and Amesz 1974; Crofts and Wraight 1983).
The exchange of fully reduced QB with the PQ
molecule from the PQ pool in the thylakoid membrane is described by two reactions. After QB
2sequentially receives two electrons from QA , QB is
protonated to form QBH2. For simplicity, this model
assumes that protonation of Q2B is instantaneous.
Effects due to the bicarbonate being bound on the
non-heme iron between QA and QB (Shevela et al.
2012) have been ignored in our model. After protonation of Q2B , QBH2 is released from the QB site of D1
protein in the PSII core, and a PQ molecule from the
PQ pool binds to the empty QB site of the PSII core
(Lazár and Jablonský 2009).
123
PQH2
Cyt b6f
charge recombination process in a PSII reaction center. P680 is the
PSII reaction center; Pheo is the pheophytin—primary electron
acceptor in PSII; S1,S2, S3, and S4 (S0) represent the four states of the
oxygen evolving complex (OEC). Yz is the tyrosine 161 in D1 protein
of PSII, which is the electron donor to P680?; QA is the first quinone
electron acceptor in PSII; QB is the second quinone electron acceptor
in PSII; E is the empty QB-pocket; PQ is the plastoquinone; PQH2 is
the plastoquinol
(5)
(6)
An increase of the chlorophyll fluorescence during
the I–P rise phase has been suggested to reflect a
‘‘traffic jam’’ around PSI (Kautsky et al. 1960;
Munday and Govindjee 1969; Stirbet and Govindjee
2012). In our current model, we have simplified
the detailed description of electron transfer process around Cyt b6f and PSI to be one single
PQH2-oxidation reaction. Further, we have included
in our model PSI simply as an electron acceptor
pool, which can only accept a limited number of
electrons, i.e., a ‘‘traffic jam’’ around PSI will take
place when this pool is fully reduced and can no
longer accept additional electrons.
The electron donation to P680? through Yz is
described using the Kok model (Kok et al. 1970).
Specifically, the OEC complex is bound to the PSII
Photosynth Res
core, i.e., one OEC complex can only transfer
electrons to the particular PSII it binds to. Transitions between the four different states, i.e., S0 ? S1
? S2 ? S3 ?S0 (S4) ? S1, are explicitly modeled.
(7) The PSII units can not only have PQ pools of
different sizes, but also antenna of different sizes;
PSIIs can also be categorized into QB-reducing and
QB-nonreducing PSII centers (Lavergne 1982;
Guenther and Melis 1990; Krause and Weis 1991;
Melis 1991; Lavergne and Trissl 1995; Lavergne
and Briantais 1996; Lazár 2003). Strasser
(1978, 1981) has suggested that different PSII units
may differ in their architecture in terms of sharing
antenna around them. However, to simplify our
model, we have considered only the heterogeneity
of PSII in terms of the QB-reducing and
QB-nonreducing centers. This model assumes that
the QB-nonreducing centers have a smaller antenna
size than the QB-reducing centers (Chylla and
Whitmarsh 1990; Strasser and Stirbet 1998; Zhu
et al. 2005) and one PSII unit is served by one
independent PQ pool. According to the previous
studies that the fraction of QB-nonreducing PSII
should be \10 % (Stirbet and Govindjee 2012). Our
model further assumes that the QB-nonreducing PSII
in each PSII group is different and there are 5 %
QB-nonreducing PSII in the entire pool, i.e.,
thousands of PSII groups.
(8) The excitation energy transfer among PSII units is
described using the ‘‘pebble-mosaic’’ model (Sauer
1975). A closed reaction center is defined as a PSII
reaction center in which the electron acceptor QA is
reduced. The model assumes a connectivity parameter p of 0.55 to be the probability of the migration
of excitation energy from the antenna of a closed
reaction center to that of an open reaction center in
the same group (i.e., Scheme 1b). In other words,
we have assumed that the excitation energy can only
be transferred within a group, which includes a
limited number of PSII units.
(9) In this model, the PSII units are organized into
groups (see Scheme 1), simulations are conducted
for each PSII group individually, and then the results
from hundred thousand individual PSII groups are
summed up to give the final results.
(10) The variable chlorophyll a fluorescence is assumed
to originate from PSII antennae, since the contribution of PSI to the variable fluorescence is very small
(Govindjee 2004).
(11) Schansker et al. (2011, 2013) reported that the
fluorescence yield is not only determined by the QA
redox state but also by a light-induced conformational change within PSII during FI. Currently, our
model does not incorporate this conformational
change. The chlorophyll a fluorescence is calculated
based on the redox state of QA. This is in agreement
with the approach taken in earlier studies (Duysens
and Sweers 1963; Joliot and Joliot 1964; Lavergne
and Trissl 1995; Stirbet et al. 1998; Lazár 1999,
2009; Lazár and Jablonský 2009). Thus, the relative
variable fluorescence is calculated as:
V ðtÞ ¼ ð1 pÞBðtÞ=ð1 pBðtÞÞ
ð1Þ
where the simulated V(t) can be compared with the experimental V(t) = (F(t) – F0)/(FM - F0); B(t) is a relative
amount of reduced QA (between 0 and 1), p is the connectivity
parameter which represents the probability of the migration of
excitation energy from the antenna of a closed reaction center
to that of an open reaction center in the same group.
(12) Given that the electric field only influences the FI
under low and medium light intensities (Lebedeva
et al. 2002), we have assumed, in the current model,
that there is no effect of the transmembrane electric
potential on reaction rate constants during a dark to
high light transition.
(13) As shown experimentally by (Tóth et al. 2005),
fluorescence quenching by PQ probably does not
occur in vivo, although it can be observed in
thylakoid and PSII membrane preparations
(Vernotte et al. 1979; Kurreck et al. 2000; Tóth
et al. 2005). Therefore, PQ quenching was not
considered in this model.
(14) The P680? quenching was not considered in this current
model because there is no significant accumulation of
P680? under most conditions (Dau 1994).
The rule-based kinetic Monte Carlo algorithm
A rule-based KMC algorithm was developed by Yang et al.
(2008) for simulating the biochemical reactions in complex
cellular signaling systems. In this method, a rule includes
several pieces of information, i.e., the molecular components
involved in a transformation, how these components change,
conditions that affect whether a transformation occurs, and a
rate law describing the dependence of the reaction rate on its
substrate concentrations. The basic workflow, as well as a
simple example, is given in Scheme 2. Given that this
algorithm has not been used by the photosynthesis research
community, we describe in detail how to use this algorithm
to simulate a simple biological system.
The test system includes a set of PSIIs, P ¼ fPSII1 ;
. . .; PSIIN g, where each PSII is comprised of a set of electron
transfer components C ¼ fOEC; Yz ; . . .g, and these components C can have different states S ¼ fS1 ; . . .; Sn g. In this
system, the electron transfer between different components is
123
Photosynth Res
Scheme 2 Diagram of the rulebased kinetic Monte Carlo
algorithm. a The workflow of
this algorithm; rtot is the total
reaction rate of the whole
system; q1 , q2, and q3 are three
uniform random variables; m is
the total number of rules; rj is
the reaction rate of reaction (or
rule) j; s is the waiting time to
the next reaction to occur; VJ is
the maximum rate of reaction
(or rule) j. b An example
illustrating the workflow of the
rule-based kinetic Monte Carlo
algorithm. In this example, this
algorithm was used to describe
the electron transfers from A to
B, from A to C, and from D to
A. Each step of (b) matches a
step in the (a) (e.g., step 1 of
(b) was the example of step 1 in
(a)). k1 is the reaction rate for
rule 1; k2 is the reaction rate for
rule 2; and k3 is the reaction rate
for rule 3. k1 = 100, k2 = 200,
and k3 = 300
a
b
List all possible reactions and give
a unique rule ID to each reaction
Initialize the molecular states, the
starting time t, the stop time Tend
Calculate the total reaction rate
according to each reaction rule j:
Rtot = r1 + r2 + r3
j =1
= 6000
Sample the waiting time,
ρ1 = 0.2245; ρ 2 = 0.4214
τ = −(
1
) ln( ρ1 )
rtot
m
j
1
) ln( ρ1 )
rtot
= 0.00024898
Select a rule RJ by finding the
smallest integer J that satisfies
j =1
There are 10 A-B, 10
A-C and 10 A-D at
time 0. t = 0,
= 10k1 + 10k2 + 10k3
Sample two uniform random
variables:
∑r
ABACA-D
m
Rtot = ∑ rj
τ = −(
Rule 1: A-B
Rule 2: A-C
Rule 3: AD-
m
∑ r = r + r >ρ r
j
1
2
2 tot
j =1
Rule 2 was selected
> ρ 2 rtot
According to Rule 2:
1 A-C turn to ACMake the reaction J, and update
the molecular states according to
the rule J
t = 0 + 0.00024898
t < Tend
t < Tend
t ≥ Tend
Stop
described as a set of reaction rules R (see Table 3 in
‘‘Appendix’’). To use the KMC algorithm, the system needs to
be initialized first, i.e., the initial state of each electron transfer
components, as well as the start time t and the stop time Tend
should be set (Step 1). After this, the reaction rate of each
reaction is calculated according to the defined set of rules R
(Step 2). Each reaction in the system occurs at a discrete time
step. The waiting time, s, to the next event is given by
s ¼ ð1=rtot Þ lnðq1 Þ
ð2Þ
P
where rtot ¼ m
j¼1 rj , m is the total number of rules, which
is the total number of reactions involved, rj is the reaction
123
rate of the rule (or reaction) j and q1 2 ð0; 1Þ is a uniform
random number (Step 3). Then, a rule Rj = J is selected by
finding the smallest integer J that satisfies
J
X
rj [ q2 rtot
ð3Þ
j¼1
where q2 2 ð0; 1Þ is a second uniform random number
(Step 4). Then, the particular reaction Rj = J is applied.
The time is updated by setting t = t ? s (Step 5).
After this step, if the stopping criterion is not satisfied
(e.g., t \ Tend), the algorithm iterates back to the
step 2.
Photosynth Res
One of the advantages of this rule-based KMC method is its
ability to describe a particular reaction with the states of only the
compounds immediately involved in the reaction (Yang et al.
2008). For example, the charge separation in an open PSII unit
is described by the rule ‘‘P680*PheoQA ? P680?Pheo-QA’’.
During simulation, the algorithm only needs to check the states
of P680, Pheo, and QA of each PSII unit, the states of other
components in the system, e.g., OEC and QB, though linked to
P680 and QA, do not influence the calculation of rate of the
charge separation. As a result, the rule ‘‘P680*PheoQA ?
P680?Pheo-QA’’ represents the reaction taking place in many
possible configurations of PSII units where the states of OEC
and QB differ. This advantage of the rule-based KMC has
enabled us to construct the entire electron transport in our
model. This model includes seven PSII electron carriers (i.e.,
OEC, Yz, P680, Pheo, QA, QB, PQ pool, and the simplified PSI
acceptor pool), each having a number of different states, i.e.,
OEC with four states (S1, S2, S3, S0), Yz with two states
(Yz, Yz?), P680 with three states (P680, P680?, P680*), Pheo with
two states (Pheo, Pheo-), QA with two states (QA, QA ), QB with
2four states (QB, Q,
Q
,
E;
where
E
means
an
empty
QB-site)
B
B
and the PSI pool acceptor with several states (i.e., the PSI
acceptor pool can still accept 1, 2, 3, … electrons). If a photosystem with different combinations of the particular redox
states of the six electron carriers of PSII would be modeled by
an ODE system, a total of 4 9 2 9 3 9 2 9 2 9 4 = 384
PSII configurations would have to be simulated. Furthermore,
since complex excitation energy transfer processes take place
among different PSII units, and there are PSII units with different PSI pool states, developing an ODE system of such a
complex model will be practically impossible. Here, with the
rule-based KMC method, we can define all these reactions with
only 36 rules. The entire set of rules is detailed and listed in
Table 3 in ‘‘Appendix’’.
In this study, each PSII group was independently simulated.
Simulation results for 100,000 independent PSII groups were
summed up to generate the final result. Each group includes a
defined number of PSII units. The parameters (e.g., reaction
rates, PQ pool sizes, PSI acceptor pool sizes, and antenna
sizes.) used in this model are listed in Table 1. However, different from the previous models, the current model uses a range
of rate constants instead of a fixed rate constant to account for
the variability of the reported values of rate constants.
Results
20–30 ms, and a maximal level of the fluorescence, which is
reached at about 80 ms. These positions of the intermediary
dips and the peak of the simulated FI curve agree relatively
well with those observed in the experimental FI curve (Fig. 1).
Table 2 lists the time positions and the levels of the O, J, I, and
P steps, as predicted by earlier models. Both the time points
and the relative fluorescence levels at the J and I steps, predicted by this current model, are close to the experimental
ones. The time point of the J step was also predicted well by
most of the earlier models (Stirbet et al. 1998; Lazár 2003,
2009); however, we note that the I–P phase had not been
accurately predicted by most of the earlier models except that
the model of Lazár (2009) had predicted a rise to the I step. The
I step was correctly simulated by Lazár (2003) and Zhu et al.
(2005), but that it was at the same time as their FM (P step).
Most of those also predicted an earlier peak (P) of the FI curve
compared to the experimental data (see Table 2).
We also simulated the FI for leaves treated with different electron transfer inhibitors, i.e., DCMU and DBMIB,
or the PSI electron acceptor MV. DCMU is a well-known
inhibitor of the electron transfer from QA to QB (Velthuys
1981) because it competitively binds to the QB-site
(Oettmeier and Soll 1983; Trebst and Draber 1986; Trebst
1987). DBMIB inhibits the reoxidation of PQH2 by Cyt b6/f
(Trebst 2007) and MV is a compound which accepts electrons from PSI (Munday and Govindjee 1969; Schansker
et al. 2005; Tóth et al. 2007).
In this work, the DCMU treatment was simulated by
setting the rates of the reactions beyond QA, i.e., the
electron transfer from reduced QA to QB, and the exchange
of QBH2 with PQ, to be zero. The DBMIB treatment was
simulated by setting the rates of PQH2/PQ oxidation/
reduction to be zero, and the MV treatment by setting the
PSI acceptor pool as infinite. The results show that the
simulated FI curves obtained for different treatments were
relatively similar to the experimental curves (Fig. 2).
The effect of different light intensities on FI kinetics was
also simulated with this model. Previous studies have shown
that the relative levels of J and I steps were light intensity
dependent; in particular, the fluorescence levels at the J and
the I step decreased with decreasing light intensity, with the
J step disappearing under low light intensity (Strasser et al.
1995). In the current model, the measuring light intensity is
described by the excitation rate constant KL. In agreement
with the experimental data, our results show that the J step
disappeared and I step decreased under low light (Fig. 3).
Comparison between simulated and measured FI curves
Potential mechanisms underlying the OJIP kinetics
A typical experimental FI curve shows a J step around 1–2 ms,
a I step around 20–30 ms, and the P step around 150–500 ms
(Strasser and Govindjee 1992; Strasser et al. 2004). The predicted FI curve shows a dip around 2 ms, another dip around
The influence of different structural and biochemical parameters on FI kinetics has been studied here using this new model.
Our results show that the increase of the electron transfer rate
123
Photosynth Res
Table 1 Parameters used in the model
Description
Value used
Reference
Rate constant of transition from S0 to S1 state
16,700–25,000 s-1
Razeghifard et al. (1997)
Rate constant of transition from S1 to S2 state
11,800 s-1
Razeghifard et al. (1997)
Rate constant of transition from S2 to S3 state
3,300 s-1
Razeghifard et al. (1997)
Rate constant of transition from S3 to S0 state
1,330 s-1
Razeghifard et al. (1997)
Rate constant of P680? reduction by Yz in the S0 and S1 states of
OEC
5.0 9 107 s-1
Brettel et al. (1984)
Rate constant of electron transfer from P680 to Yz? in the S0 and S1
states of OEC
1.7 9 106 s-1
Brettel et al. (1984), Lazár (2003)
Rate constant of P680? reduction by Yz in the S2 and S3 states of
OEC
1.18 9 107 s-1
Brettel et al. (1984), Lazár (2003)
Rate constant of electron transfer from P680 to Yz? in the S2 and S3
states of OEC
3.95 9 106 s-1
Brettel et al. (1984), Lazár (2003)
Rate constant of charge separation in an open PSII reaction center
3.0 9 109 s-1
Dau (1994)
and Pheo in
3.0 9 108 s-1
Dau (1994)
Rate constant of charge separation in a closed PSII reaction center
4.8 9 108 s-1
Dau (1994)
3.4 9 108 s-1
Dau (1994)
2.3 9 109 s-1
Dau (1994)
2,500–5,000 s-1
Lazár (1999, 2003)
125–250 s-1
Lazár (1999, 2003)
1,250–3,300 s-1
Lazár (1999, 2003)
25–66 s-1
Lazár (1999, 2003)
Rate constant of unbinding of QBH2 from PSII
1,500 s-1
Model estimate cf. Lazár (1999), Lazár and Jablonský
(2009)
Rate constant of binding of PQH2 (QBH2) to PSII
1,500 s-1
Model estimate cf. Lazár (1999), Lazár and Jablonský
(2009)
Rate constant of binding of PQ (QB) to PSII
1,500 s-1
Model estimate cf. Lazár (1999), Lazár and Jablonský
(2009)
Rate constant of unbinding of QB from PSII
1,500 s-1
Model estimate cf. Lazár (1999), Lazár and Jablonský
(2009)
Rate constant of PQH2 oxidation in the thylakoid membrane
30 s-1
Crofts et al. (1993), Lazár and Jablonský (2009)
Rate constant of PQ reduction in the thylakoid membrane
30 s-1
Crofts et al. (1993), Lazár and Jablonský (2009)
Rate constant of non-radiative charge recombination between
P680? and Pheo- in a closed PSII reaction center
1.0 9 109 s-1
Dau (1994)
Rate constant of charge recombination between P680? and QA
10,000 s-1
Haveman and Mathis (1976), Renger and Wolff (1976)
Rate constant of heat dissipation of excitation energy in PSII
antenna
5.0 9 108 s-1
Dau (1994)
Rate constant of fluorescence emission from excited chlorophylls
in PSII antenna
6.7 9 107 s-1
Rabinovich and Govindjee (1969)
Number of photons received per chlorophyll per second
14 s-1
Lazár and Pospı́šil (1999), Lazár (2003)
Rate constant of excitation energy transfer from PSII antenna to
P680
7.6 9 1010–
2.4 9 1011 s-1
Holzwarth et al. (2006)
Rate constant of excitation energy transfer from P680 to PSII
antenna
1.44 9 1011–
2.4 9 1011 s-1
Holzwarth et al. (2006)
Rate constant of excitation energy transfer form a closed PSII
reaction center to open PSII reaction center
1.0 9 109 s-1
Lavergne and Trissl (1995), Trissl and Lavergne (1995)
The number of chlorophylls in the antenna of an QB-reducing PSII
center
290
Hall and Rao (1999)
The initial S1:S0 ratio of OEC states under normal physiological
conditions
0.75:0.25
Kok et al. (1970), Messinger and Renger (1993),
Haumann and Junge (1994)
The percentage of QB-nonreducing PSII center under normal
physiological conditions
5%
Tomek et al. (2003)
The probability of the excitation energy transfer from a closed
reaction center to an open reaction center
0.55
Lazár and Jablonský (2009)
Rate constant of charge recombination between
an open PSII reaction center
P680?
Rate constant of radiative charge recombination between
Pheo- in a closed PSII reaction center
-
P680?
and
Rate constant of electron transfer from Pheo- to QA
Rate constant of electron transfer from
Rate constant of electron transfer from
Rate constant of electron transfer from
Rate constant of electron transfer from
123
QA to QB
QB to QA
QA to QB
2QB to QA
Photosynth Res
Fig. 1 Comparison between the simulated chlorophyll a florescence
induction FI curve and the experimental data. The experimental data
were measured with a PEA fluorometer under 3,400 lmol m-2 s-1
photons of red light at room temperature. The experimental data is
from Lazár (2003) where more details of the measurements can be
found. The parameters used in this simulation are listed in Table 1.
V(t) = (F(t) – F0)/(FM – F0)
from the reduced QA to QB, or of the QBH2/PQ exchange rate
at the QB site lead to a lower fluorescence level at step
J (Fig. 4a, b). The O–J phase disappears when the electron
transfer rate from the reduced QA to QB, becomes very fast (e.g.,
20 times faster than in the control, Fig. 4a). Increasing the
fraction of the QB-nonreducing PSII also led to a higher J step
and higher J–P phase (Fig. 5). Increasing the reaction rate of
PQH2 oxidation led to an early I step and P step and a lower
fluorescence level at I step (Fig. 4c). A fast PQH2 oxidation
reaction eliminated the I step (Fig. 4c). Decreasing the PSI pool
size led to a shorter plateau of I step and an early P step
(Fig. 4d).
The effect on FI curve of the number of PSII units
in a group
We further explored the influence of the number of PSII
units in a group on the FI kinetics. As we mentioned
Fig. 2 Comparison of the simulated chlorophyll a fluorescence
induction (FI) curves with experimental data under different treatment
conditions. a The control experimental data. b The predicted data. For
3-(3,4-dichlorophenyl)-1,1-dimethylurea (DCMU) treatment, the
experimental data were measured with a PEA fluorometer under
3,400 lmol m-2 s-1 photons of red light at room temperature after
DCMU treatment. The experimental data are from Lazár (2003)
where more details of the measurements can be found; for 2,5dibromo-3-methyl-6-isopropyl-p-benzoquinone (DBMIB) treatment
and methyl viologen (MV) treatment, the experimental data were
measured with a dual channel PEA Senior instrument under
1,800 lmol m-2 s-1 photons of red light at room temperature after
DBMIB treatment and MV treatment. The experimental data are from
Schansker et al. (2005) where more details of the measurements can
be found
Table 2 Comparison of the major parameters of O, J, I, and P steps of different models of fluorescence induction
Time(J)
V(J)
Time(I)
V(I)
Time(P)
Experimental data
This model
1–2 ms
2 ms
0.38–0.4
0.38–0.4
20–30 ms
20–30 ms
0.8
0.8
150–500 ms
90 ms
Lazár (2009)
2–4 ms
0.52–0.54
30 ms
0.9
100 ms
Zhu et al. (2005)
2–3 ms
0.76–0.78
Null
Null
30 ms
Lazár (2003)
1–3 ms
0.31–0.34
Stirbet et al. (1998)
0.7–1 ms
0.4–0.43
Null
Null
30 ms
4–8 ms
0.81
30 ms
Experimental data is from literature (Strasser et al. 2004; Strasser and Govindjee 1992)
Time(J) the time of appearance of the J step, Time(I) the time of appearance of the I step, Time(P) the time of appearance of the step P, V(J) the
relative fluorescence level at the J step, V(I) the relative fluorescence level at the I step
123
Photosynth Res
Fig. 3 The simulated FI under different measuring light intensities.
V(t) = (F(t) – F0)/(FM – F0)
Fig. 5 The predicted influence of QB-nonreducing PSII centers
proportion on the shape of the chlorophyll a fluorescence induction
curve
Fig. 4 The predicted influence of different structural and kinetic
parameters on the shape of the chlorophyll a fluorescence induction
curve. a The electron transfer rate from QA to QB; b the reaction rate
of QBH2/PQ exchange at the QB site; c the rates of PQH2/PQ
oxidation/reduction through the Cyt b6f; d the pool size of the PSI
acceptor pool
123
Photosynth Res
Fig. 6 The predicted chlorophyll a fluorescence induction curves for
different group sizes of connected PSIIs. V(t) = (F(t) – F0)/(FM – F0)
earlier, we organized the PSII units into different groups in
which the excitation energy can be transferred from a
closed PSII to an open PSII (see Scheme 1). Figure 6
shows that increasing the number of PSII units in the group
(g) leads to an increased fluorescence at both J and I steps.
The predicted FI at g = 5 is closest to the experimentally
recorded FI.
Discussion
Novel features of the current model
This model includes several novel features compared to the
previous models (e.g., Lazár et al. 1997; Stirbet et al. 1998;
Lazár 2003; Zhu et al. 2005). First, here, we have considered
the fact that the electrons can only be transferred from an
electron donor to an electron acceptor within the same
photosystem. Further, we have assumed that the PSII population is organized spatially in groups that restrict the
energetic connectivity within the group but no energy
transfer between groups, i.e., the so-called ‘‘pebble mosaic’’
model (Sauer 1975) (see Scheme 1). Second, this model
incorporates a more detailed description of the electron
transfer reactions in PSII. For example, the QBH2/PQ
exchange is described by two subsequent reactions, and the
reactions taking place in the OEC have been modeled in
detail. Third, the electron transfer reactions beyond PQ pool
have been simplified to a PSI acceptor pool that can only
accept a limited number of electrons.
With the considerations mentioned above, this model
simulates the OJIP transient more realistically than the
earlier models (with the possible exception of the model by
Lazár 2009). Both the relative fluorescence levels and the
time of appearance of the J, I, and P steps agree relatively
well with the experimental data (Fig. 1; Table 2). Most of
the previous models (e.g., Stirbet et al. 1998; Lazár 2003;
Zhu et al. 2005) could not predict the I–P phase accurately,
e.g., the predicted P step in Lazár (2003) is actually the
I step and the I–P phase was missing. Although, the rise
time to the I step predicted by Lazár (2009) agreed with
experimental data, yet the J and I steps were not very
pronounced and the relative fluorescence levels at the I step
was slightly higher than in the experimental data (Table 2).
According to (Tóth et al. 2005), fluorescence quenching by
PQ probably does not occur in vivo; thus the PQ quenching
was not considered in our model. However, in previous
models the PQ quenching was used, which slowed down
the fluorescence rise (e.g., Lazár 2003; Zhu et al. 2005).
The fluorescence kinetics in this new model, compared
with the other models, was slowed down because we have
considered in our model that the PQ pool is not only
reduced by PSII, but also reoxidized (by PSI, which is not
explicitly stated in the model) during a certain period of
time. While this feature (i.e., PQ-pool reoxidation) was
present in the earlier models of Stirbet and Strasser (1995)
and Stirbet et al. (1998), in which the rate of PQ-pool
reoxidation was considered to take place indefinitely. In a
way, these models were rather simulating the interaction
with an artificial electron acceptor.
FI kinetics in the presence of different electron transfer
inhibitors (DCMU and DBMIB) and electron acceptor
(MV) treatment, and under different measuring light
intensities, were also relatively well predicted with this
model (Figs. 2, 3). The effects of DBMIB and MV treatment on the FI curves were first simulated, in a satisfactory
way, by Lazár (2009). However, there was still some difference between the current simulated and the experimental
FI curves. For example, the simulated FI showed more
pronounced J dips and an early P step (Fig. 1); the simulated DCMU FI curve is faster than the experimental curve
(Fig. 2). The reason for such differences might be that (1)
the limited assumption of the PSII heterogeneities, e.g., the
heterogeneities of the PSII antenna size was not considered
in this model; (2) the limited assumption of the factors
which could affect the FI, e.g., the light-induced conformational change within PSII during FI (Schansker et al.
2011, 2013) was not considered in this current model.
Potential mechanisms of, and factors, influencing
chlorophyll FI curve
The effects of the electron transport rate from QA to QB on
FI have been analyzed with our model, presented in this
paper. In agreement with Lazár (2003), our results show
that decreasing the electron transport rate from QA to QB or
decreasing the QBH2/PQ exchange rate at QB site led to an
123
Photosynth Res
increased J step (Fig. 4a, b). The increased J step was
caused by an accumulation of QA due to slower electron
transfer from Qto
Q
/Q
(Fig.
4a).
A
B
B
Since the QB-nonreducing PSII center cannot reduce
QB and PQ pool (Graan and Ort 1984; Whitmarsh and
Ort 1984; Melis 1985; Graan and Ort 1986; Mccauley
and Melis 1987; Chylla and Whitmarsh 1989; Lavergne
and Leci 1993), the average QA to QB electron transfer
rate of the total PSII units pool, i.e., thousands of PSII
units, is decreased when the fraction of QB-nonreducing
PSII center is increased. Our results show that increase
of the percentage of QB-nonreducing PSII center also
leads to an increased J step (Fig. 5), and those increases
show a similar pattern as that caused by decreases in the
electron transfer rate from QA to QB (Fig. 4a). Based on
the experiments of Tóth et al. (2005), Stirbet and Govindjee (2012) suggested that the J–I–P phase is caused
by the reduction of oxidized PQ from the PQ pool. This
conclusion is confirmed here through simulations using
the current model. Our results show that the rise time to
I step is influenced by the rate constants of PQH2 oxidation and PQ reduction (Fig. 4c). Stirbet and Govindjee
(2012) suggested that the length of the plateau (and/or
dip) around the I phase depends on the size of the PSI
pool of electron acceptors. In agreement with this opinion, this current model shows that the duration around
the I plateau was influenced by the PSI acceptor pool
size a smaller PSI pool led to a shorter duration of the I
plateau (Fig. 4d).
Previous studies (Kautsky et al. 1960; Munday and
Govindjee 1969) suggested that the P level is caused by a
block in the oxidation of the reduced electron acceptors in
PSI, i.e., there is a ‘‘traffic jam’’ of electrons at the electron
acceptor end of PSI. By simultaneously measuring the FI
and the 820-nm transmission change, Schansker et al.
(2003, 2005) suggested that I–P phase was caused by the
inactivation of Ferredoxin–NADP reductase (FNR) in a
dark adapted leaf. This conclusion was supported by this
current model as well as by the model developed by Lazár
(2009). We note that Lazár (2009) had not only considered
the PSI pigment protein complexes and the electron
transport components around PSI, i.e., plastocyanin (PC),
ferredoxin (Fd), and FNR but also Cyt b6f and the cyclic
electron transport (CET) around PSI. In contrast to the
model of Lazár (2009), our current model has simplified all
the components beyond PQ pool as a PSI acceptor pool,
which can accept a finite number of electrons, so that all
the electron transport reactions beyond PQ are represented
by one reaction, which oxidizes PQH2. The ability of this
simplified model to predict FI kinetics indicates that the
modeling of the detailed molecular mechanisms taking
place in Cty b6f and PSI not absolutely necessary in order
to simulate the FI kinetics.
123
The influence of the number of PSII units in a group
on FI kinetics
A major feature of the current model is that, instead of
allowing excitation energy transfer between all the PSII
units as in previous models (Stirbet et al. 1998; Lazár
2003; Zhu et al. 2005), the excitation energy can only
migrate among a limited numbers of PSII units in one
group. Result shows that the PSII connectivity is simulated well with this model (Supplementary Fig. 1). With
this feature, the model has been used to explore the
influence of the number of PSII units in a group on FI
kinetics. In agreement with a previous study (Trissl and
Lavergne 1995), our simulated results show that the FI
curves obtained for 4 or 5 PSII fit well with the
experimental FI curve (Fig. 6.) Increasing the number of
PSII units in a group from 5 to 7 led to a shorter J–
I step and a higher I phase (Fig. 6). One caveat that has
not been considered in the current model is that there
might be different PSII groups each with different
number of PSII units and even varying number of PSII
units under different conditions (Strasser and Stirbet
1998).
Conclusions
By using a KMC algorithm, we have developed a FI model
that incorporates structural information on PSII and its
associated components. Compared to the previous models,
the new model has improved the accuracy of the prediction
of the OJIP kinetics; in particular, it has improved the
prediction of the relative level and rise time to the J, I, and
P steps. Using this model, we have examined the potential
processes underlying different phases of the OJIP kinetics
and the influence of different structural and biophysical
features on the fluorescence rise kinetics. Our results suggest that (1) the J step is caused by the limitation of
electron transport between QA and QB, i.e., the TEG at the
QB site; (2) the I step is caused by the rate limitation of the
PQH2 re-oxidation; (3) the P step is caused by a block in
the oxidation of the reduced electron acceptors in PSI. In
summary, our new model provides a framework for
exploring the impact of modifying not only kinetic but also
structural parameters on FI kinetics.
Acknowledgments This work is dedicated to Professor Govindjee
who is an influential teacher of many aspects of photosynthesis
research, particularly in the use of chlorophyll fluorescence in
studying biophysics of photosynthesis. This research was funded by
the National Science Foundation of China NSFC30970213,
NSFC30870477, the Max Planck Society and the Chinese Academy
of Sciences. We thank Dr. Danny Tholen for comments on the
manuscript and Song Feng for help in the programming.
Photosynth Res
Appendix
See Tables 3 and 4.
Table 3 The rules used in the rule-based kinetic Monte Carlo algorithm that describe the reactions associated with the QB-reducing PSII
reaction centers and the excitation energy transfer from closed to open PSII reaction centers
Rules
Description
OEC_S0Yz? ? OEC_S1Yz
Electron transfer from OEC to Yz and the transition of OEC from S0 to S1
OEC_S1Yz? ? OEC_S2Yz
Electron transfer from OEC to Yz and the transition of OEC from S1 to S2 state
OEC_S2Yz? ? OEC_S3Yz
Electron transfer from OEC to Yz and the transition of OEC from S2 to S3 state
OEC_S3Yz? ? OEC_S0Yz
Electron transfer from OEC to Yz and the transition of OEC from S3 to S0 state
OEC_S0YzP680? ? OEC_S0Yz?P680
OEC_S1YzP680? ? OEC_S1Yz?P680
OEC_S2YzP680? ? OEC_S2Yz?P680
OEC_S3YzP680? ? OEC_S3Yz?P680
OEC_S0Yz?P680 ? OEC_S0YzP680?
OEC_S1Yz?P680 ? OEC_S1YzP680?
OEC_S2Yz?P680 ? OEC_S2YzP680?
OEC_S3Yz?P680 ? OEC_S3YzP680?
P*680PheoQA ? P680?Pheo-QA
P680?Pheo-QA ? P*680PheoQA
Electron transfer from Yz to P680? when OEC is in the S0 state
?
- P*680PheoQA ? P680 Pheo QA
Primary charge separation in a closed PSII reaction center
P680?Pheo-QA ? P680*PheoQA
Charge recombination in a closed PSII reaction center leading to formation of P680
in its excited state
P680?Pheo-QA ? P680PheoQA
Charge recombination in a closed PSII reaction center leading to the ground state of
P680 and Pheo
Pheo-QA ? PheoQA
Electron transfer from Pheo- to QA
QA QB
Electron transfer from QA to QB
? QAQB
-
-
QAQB ? QA QB
2QA QB ? QAQB
2QAQB
? QA QB PSII_QBH2 2- ? PSII_E
Electron transfer from Yz to P680? when OEC is in S1 state
Electron transfer from Yz to P680? when OEC is in S2 state
Electron transfer from Yz to P680? when OEC is in S3 state
Electron transfer from P680 to Yz? when OEC is in S0 state
Electron transfer from P680 to Yz? when OEC is in S1 state
Electron transfer from P680 to Yz? when OEC is in S2 state
Electron transfer from P680 to Yz? when OEC is in S3 state
Primary charge separation in an open PSII reaction center
Charge recombination in an open PSII reaction center leading to formation of P680
in its excited state
Electron transfer from QB to QA
Electron transfer from QA to QB
Electron transfer from Q2B to QA
? PQH2
Releasing of QBH2 from the QB-pocket
PSII_E ? PQH2 ? PSII_QBH2
Binding of QBH2 to the QB-pocket
PSII_E ? PQ ? PSII_QB
PSII_QB ? PSII_E ? PQ
Binding of PQ to the empty QB-pocket in PSII
Releasing of PQ from the QB-pocket in PSII
PQH2 ? PQ
Oxidation of PQH2 molecules in the thylakoid membrane by PSI pool via the Cyt
b6f
PQ ? PQH2
Reduction of oxidized PQ molecules in the thylakoid membrane by the Cyt b6f
A_Chl ? A_Chl*
Formation of excited states of Chl in the PSII antenna
A_Chl* ?A_Chl ? F
Dissipation of excitation energy in PSII antenna as fluorescence
A_Chl* ? A_Chl ? H
Dissipation of excitation energy as heat
A_Chl*P680 ? A_ChlP680*
Excitation energy transfer from PSII antenna to reaction center
A_ChlP680* ? A_Chl*P680
Excitation energy transfer from reaction center back to PSII antenna
P680?QA ? P680*QA
Charge recombination between P680? and QA leading to formation of P680 in its
excited state
PSII_C_A_Chl* ?PSII_O_A_Chl ?
PSII_C_A_Chl ? PSII_O_A_Chl*
Excitation energy transfer from a closed PSII reaction center to an open PSII
reaction center
123
Photosynth Res
Table 4 The definition of mathematical expressions used in the paper
Mathematical
expressions
Description
P ¼ fPSII1 ; . . .; PSIIN g
The PSII set P is constituted by N PSII units i.e. PSII1, PSII2, …, PSIIN
C ¼ fOEC; Yz ; . . .g
The electron transfer components set C is constituted by different electron transfer components i.e. OEC, Yz…
S ¼ fS1 ; . . .; Sn g
The electron transfer components states set S is constituted by different states of each electron transfer components,
e.g. the P680 states set is constituted by P680, P680?, P680*, i.e. S_P680 = {P680, P680?, P680*}
Sum of rj, r2,.. rJ
J
P
rj
j¼1
q[(0,1)
q is a number with a value between 0 and 1, but does not include 0 and 1, i.e., 0 \ q \1
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