REGULAR PAPER

A model of chlorophyll a fluorescence induction kineticswith explicit description of structural constraints of individualphotosystem 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) kinet-

ics, 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 simpli-

fied 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 treat-

ment, 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 two-

electron gate at the QB site; (2) the I step is caused by the rate

limitation of the plastoquinol re-oxidation in the plastoqui-

none 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-p-

benzoquinone

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

This manuscript is written in honor of Professor Govindjee for his

monumental contributions to photosynthesis research and education.

Electronic supplementary material The online version of thisarticle (doi:10.1007/s11120-013-9894-2) contains supplementarymaterial, 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

123

Photosynth Res

DOI 10.1007/s11120-013-9894-2

RCII Reaction center of photosystem II

V(t) Relative variable fluorescence (= (F(t) - F0)/

(FM - F0))

YZ 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 pho-

tochemistry after excitation energy transfer to reaction

centers, dissipation as heat, and emission as light (fluores-

cence) (Govindjee et al. 1986; Govindjee 1995, 2004; Stir-

bet 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, measur-

ing 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 chlo-

rophyll fluorescence induction (FI) curves (the Kautsky

effect) using high light intensities; in the current terminol-

ogy, 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; Lazar 2006; Lazar and Sch-

ansker 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 (Lazar 2006; Lazar 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

quinone electron acceptor QA and the second quinone elec-

tron acceptor QB, and taking into account the fact that QB can

accept two electrons (Crofts and Wraight 1983; Bouges-

Bocquet 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

Schloder (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 com-

bined 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 reac-

tions, including QB2- protonation, QBH2/plastoquinone (PQ)

exchange, and P680? reduction, were incorporated. However,

the models proposed by Baake and Schloder (1992) and Le-

bedeva 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 Lazar (2003) and Zhu

et al. (2005) were a combination of TEG, RRP, and Kok

models and they provided a detailed description of the reac-

tions around PSII to simulate the fast FI curve. However,

these two models (Lazar 2003; Zhu et al. 2005) still included a

number of assumptions that are incompatible with biological

reality. For example, Lazar (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 (Lazar and Jablonsky 2009). However, the QBH2/PQ

exchange is better described by two subsequent reactions and

the OEC being considered bound to PSII (Lazar and Jab-

lonsky 2009). Some of the models (see e.g., Zhu et al. 2005)

have ignored that the reactions within a PSII electron trans-

port chain are restricted to the same complex.

To explore the potential impacts of the spatial arrange-

ment of different components on FI, Lazar and Jablonsky

(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 reac-

tions were restricted to the same complex. This study

showed that different structural and kinetic rules can lead

to qualitatively different results (Lazar and Jablonsky

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

123

ODE-based modeling approach quickly becomes intracta-

ble. This is because with an increase in the model com-

plexity, it becomes practically impossible to enumerate all

the intermediate states of the photosynthetic system. Since

the goal of the work by Lazar and Jablonsky (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., Lazar

et al. 1997; Stirbet et al. 1998; Lazar 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 (Lazar et al.

1997; Stirbet et al. 1998; Lazar 2003; Zhu et al. 2005) have

shown that considering PSII alone is not sufficient to

simulate experimental FI curves. Lazar (2009) extended the

model of Lazar and Jablonsky (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 (Lazar 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 simpli-

fied 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 rela-

tionship 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-p-

benzoquinone (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 Lazar and Schansker 2009):

(1) 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 Schloder 1992;

Lazar 1999, 2003; Lazar and Jablonsky 2009; Lazar

2009).

(2) De-excitation of the excited state of Chl occurs

through three major pathways, i.e., (a) primary pho-

tochemistry 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.

(3) The primary photochemistry (i.e., the charge sepa-

ration, 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; Lazar

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.

Photosynth Res

123

(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 mem-

brane is described by two reactions. After QB

sequentially receives two electrons from QA-, QB

2- is

protonated to form QBH2. For simplicity, this model

assumes that protonation of QB2- 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 proton-

ation of QB2-, 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

(Lazar and Jablonsky 2009).

(5) 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 pro-

cess 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.

(6) 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

AntennaP680

PheoP680

*

PheoP680

+

Pheo-

P680

Pheo-

S1

S2

S0

S42H2O

O2 +4H+

S3

e-

e-

e-

Oxygen Evolving Complex

Heat (Yz)e-

P680+

Pheo

QAQB QA-QB QAQB

- QA-QB

- QAQB2- QA

-QB2-

QAΕ QA-

PQH2

PQ

PQ PQH2

PQ pool

Light

Fluorescence and Heat

PSIIC

ExcitedEnergy

PSIIO

PSII group

PSII group

PSII group

PSII group

PSII group PSII group

a b

P680

Pheo

c

PSI acceptorpool

Cyt b6f

Scheme 1 Diagram of the current chlorophyll a fluorescence induc-

tion 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

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

Photosynth Res

123

core, i.e., one OEC complex can only transfer

electrons to the particular PSII it binds to. Transi-

tions 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; Lazar 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 param-

eter 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 contribu-

tion 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 conforma-

tional 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; Lazar 1999,

2009; Lazar and Jablonsky 2009). Thus, the relative

variable fluorescence is calculated as:

V tð Þ ¼ 1� pð ÞB tð Þ= 1� pB tð Þð Þ ð1Þ

where the simulated V(t) can be compared with the experi-

mental 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 (Toth 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; Toth

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 PSII1;f. . .; PSIINg, where each PSII is comprised of a set of electron

transfer components C ¼ OEC;Yz; . . .f g, and these compo-

nents C can have different states S ¼ S1; . . .; Snf g. In this

system, the electron transfer between different components is

Photosynth Res

123

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 � 1=rtotð Þ ln q1ð Þ ð2Þ

where rtot ¼Pm

j¼1 rj, m is the total number of rules, which

is the total number of reactions involved, rj is the reaction

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

XJ

j¼1

rj [ q2rtot ð3Þ

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.

endt T<

Rule 1: A-B AB-

Rule 2: A-C AC-

Rule 3: AD- A-D

There are 10 A-B, 10

A-C and 10 A-D at

time 0. t = 0,

1 2 3

1 2 310 10 10

6000

totR r r r

k k k

= + += + +=

1 20.2245; 0.4214ρ ρ= =

1

1( ) ln( )

0.00024898totr

τ ρ= −

=

j 1 2 21

>m

totj

r r r rρ=

= +∑

Rule 2 was selected

According to Rule 2:

1 A-C turn to AC-

t = 0 + 0.00024898

endt T<

Stop

endt T≥

Calculate the total reaction rate

according to each reaction rule j:

1

m

tot jj

R r=

= ∑Sample two uniform random

variables:

Make the reaction J, and update

the molecular states according to

the rule J

Select a rule RJ by finding the

smallest integer J that satisfies

21

j

m

totj

r rρ=

>∑

Sample the waiting time,

1

1( ) ln( )

totrτ ρ= −

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

a bScheme 2 Diagram of the rule-

based 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

Photosynth Res

123

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*�Pheo�QA ? 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*�Pheo�QA ?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

four states (QB, QB-, QB

2-, E; where E means an empty QB-site)

and the PSI pool acceptor with several states (i.e., the PSI

acceptor pool can still accept 1, 2, 3, … electrons). If a photo-

system 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 dif-

ferent 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, dif-

ferent 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

Comparison between simulated and measured FI curves

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 pre-

dicted FI curve shows a dip around 2 ms, another dip around

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, pre-

dicted 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; Lazar 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 Lazar (2009) had predicted a rise to the I step. The

I step was correctly simulated by Lazar (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 dif-

ferent 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 elec-

trons from PSI (Munday and Govindjee 1969; Schansker

et al. 2005; Toth 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).

Potential mechanisms underlying the OJIP kinetics

The influence of different structural and biochemical parame-

ters on FI kinetics has been studied here using this new model.

Our results show that the increase of the electron transfer rate

Photosynth Res

123

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), Lazar (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), Lazar (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), Lazar (2003)

Rate constant of charge separation in an open PSII reaction center 3.0 9 109 s-1 Dau (1994)

Rate constant of charge recombination between P680? and Pheo- in

an open PSII reaction center

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)

Rate constant of radiative charge recombination between P680? and

Pheo- in a closed PSII reaction center

3.4 9 108 s-1 Dau (1994)

Rate constant of electron transfer from Pheo- to QA 2.3 9 109 s-1 Dau (1994)

Rate constant of electron transfer from QA- to QB 2,500–5,000 s-1 Lazar (1999, 2003)

Rate constant of electron transfer from QB- to QA 125–250 s-1 Lazar (1999, 2003)

Rate constant of electron transfer from QA- to QB

- 1,250–3,300 s-1 Lazar (1999, 2003)

Rate constant of electron transfer from QB2- to QA 25–66 s-1 Lazar (1999, 2003)

Rate constant of unbinding of QBH2 from PSII 1,500 s-1 Model estimate cf. Lazar (1999), Lazar and Jablonsky

(2009)

Rate constant of binding of PQH2 (QBH2) to PSII 1,500 s-1 Model estimate cf. Lazar (1999), Lazar and Jablonsky

(2009)

Rate constant of binding of PQ (QB) to PSII 1,500 s-1 Model estimate cf. Lazar (1999), Lazar and Jablonsky

(2009)

Rate constant of unbinding of QB from PSII 1,500 s-1 Model estimate cf. Lazar (1999), Lazar and Jablonsky

(2009)

Rate constant of PQH2 oxidation in the thylakoid membrane 30 s-1 Crofts et al. (1993), Lazar and Jablonsky (2009)

Rate constant of PQ reduction in the thylakoid membrane 30 s-1 Crofts et al. (1993), Lazar and Jablonsky (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 Lazar and Pospısil (1999), Lazar (2003)

Rate constant of excitation energy transfer from PSII antenna to

P680

7.6 9 1010–

2.4 9 1011 s-1Holzwarth et al. (2006)

Rate constant of excitation energy transfer from P680 to PSII

antenna

1.44 9 1011–

2.4 9 1011 s-1Holzwarth 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 Lazar and Jablonsky (2009)

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123

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. 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 Lazar (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)

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 1–2 ms 0.38–0.4 20–30 ms 0.8 150–500 ms

This model 2 ms 0.38–0.4 20–30 ms 0.8 90 ms

Lazar (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

Lazar (2003) 1–3 ms 0.31–0.34 Null Null 30 ms

Stirbet et al. (1998) 0.7–1 ms 0.4–0.43 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

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 Lazar (2003)

where more details of the measurements can be found; for 2,5-

dibromo-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

Photosynth Res

123

Fig. 3 The simulated FI under different measuring light intensities.

V(t) = (F(t) – F0)/(FM – F0)

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

Fig. 5 The predicted influence of QB-nonreducing PSII centers

proportion on the shape of the chlorophyll a fluorescence induction

curve

Photosynth Res

123

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., Lazar et al. 1997; Stirbet et al. 1998;

Lazar 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 pop-

ulation 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

Lazar 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; Lazar 2003;

Zhu et al. 2005) could not predict the I–P phase accurately,

e.g., the predicted P step in Lazar (2003) is actually the

I step and the I–P phase was missing. Although, the rise

time to the I step predicted by Lazar (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 (Toth 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., Lazar 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 treat-

ment on the FI curves were first simulated, in a satisfactory

way, by Lazar (2009). However, there was still some dif-

ference 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 simu-

lated 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 confor-

mational 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 Lazar (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

Fig. 6 The predicted chlorophyll a fluorescence induction curves for

different group sizes of connected PSIIs. V(t) = (F(t) – F0)/(FM – F0)

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123

increased J step (Fig. 4a, b). The increased J step was

caused by an accumulation of QA- due to slower electron

transfer from QA- to QB/QB

- (Fig. 4a).

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 Toth et al. (2005), Stirbet and Gov-

indjee (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 oxi-

dation 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 opin-

ion, 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 Lazar

(2009). We note that Lazar (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 Lazar (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.

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; Lazar

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 simu-

lated 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 sug-

gest 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

123

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_S0�Yz? ? OEC_S1�Yz Electron transfer from OEC to Yz and the transition of OEC from S0 to S1

OEC_S1�Yz? ? OEC_S2�Yz Electron transfer from OEC to Yz and the transition of OEC from S1 to S2 state

OEC_S2�Yz? ? OEC_S3�Yz Electron transfer from OEC to Yz and the transition of OEC from S2 to S3 state

OEC_S3�Yz? ? OEC_S0�Yz Electron transfer from OEC to Yz and the transition of OEC from S3 to S0 state

OEC_S0�Yz�P680? ? OEC_S0�Yz

?�P680 Electron transfer from Yz to P680? when OEC is in the S0 state

OEC_S1�Yz�P680? ? OEC_S1�Yz

?�P680 Electron transfer from Yz to P680? when OEC is in S1 state

OEC_S2�Yz�P680? ? OEC_S2�Yz

?�P680 Electron transfer from Yz to P680? when OEC is in S2 state

OEC_S3�Yz�P680? ? OEC_S3�Yz

?�P680 Electron transfer from Yz to P680? when OEC is in S3 state

OEC_S0�Yz?�P680 ? OEC_S0�Yz�P680

? Electron transfer from P680 to Yz? when OEC is in S0 state

OEC_S1�Yz?�P680 ? OEC_S1�Yz�P680

? Electron transfer from P680 to Yz? when OEC is in S1 state

OEC_S2�Yz?�P680 ? OEC_S2�Yz�P680

? Electron transfer from P680 to Yz? when OEC is in S2 state

OEC_S3�Yz?�P680 ? OEC_S3�Yz�P680

? Electron transfer from P680 to Yz? when OEC is in S3 state

P680* �Pheo�QA ? P680

?�Pheo-�QA Primary charge separation in an open PSII reaction center

P680?�Pheo-�QA ? P680

* �Pheo�QA Charge recombination in an open PSII reaction center leading to formation of P680

in its excited state

P680* �Pheo�QA

- ? P680?�Pheo-�QA

- Primary charge separation in a closed PSII reaction center

P680?�Pheo-�QA

- ? P680*�Pheo�QA- Charge recombination in a closed PSII reaction center leading to formation of P680

in its excited state

P680?�Pheo-�QA

- ? P680�Pheo�QA- Charge recombination in a closed PSII reaction center leading to the ground state of

P680 and Pheo

Pheo-�QA ? Pheo�QA- Electron transfer from Pheo- to QA

QA-�QB ? QA�QB

- Electron transfer from QA- to QB

QA�QB- ? QA

-�QB Electron transfer from QB- to QA

QA-�QB

- ? QA�QB2- Electron transfer from QA

- to QB-

QA�QB2- ? QA

-�QB- Electron transfer from QB

2- to QA

PSII_QBH22- ? PSII_E ? 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 Binding of PQ to the empty QB-pocket in PSII

PSII_QB ? PSII_E ? PQ 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_Chl�P680* Excitation energy transfer from PSII antenna to reaction center

A_Chl�P680* ? 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

Photosynth Res

123

References

Antal TK, Kolacheva A, Maslakov A, Riznichenko GY, Krendeleva

TE, Rubin AB (2013) Study of the effect of reducing conditions

on the initial chlorophyll fluorescence rise in the green micro-

algae Chlamydomonas reinhardtii. Photosynth Res 114:143–154

Baake E, Schloder J (1992) Modelling the fast fluorescence rise of

photosynthesis. Bull Math Biol 54:999–1021

Bouges-Bocquet B (1973) Electron transfer between the two photo-

systems in spinach chloroplasts. Biochim Biophys Acta

314:250–256

Breton J (1983) The emission of chlorophyll in vivo: antenna

fluorescence or ultrafast luminescence from the reaction center

pigments. FEBS Lett 159:1–5

Brettel K, Schlodder E, Witt HT (1984) Nanosecond reduction

kinetics of photooxidized chlorophyll aII (P-680) in single

flashes as a probe for the electron pathway, H?-release and

charge accumulation in the O2-evolving complex. Biochim

Biophys Acta 766:403–415

Chylla RA, Whitmarsh J (1989) Inactive photosystem II complexes in

leaves—turnover rate and quantitation. Plant Physiol

90(2):765–772

Chylla RA, Whitmarsh J (1990) Light saturation response of inactive

photosystem II reaction centers in spinach. Photosynth Res

25:39–48

Crofts AR, Wraight CA (1983) The electrochemical domain of

photosynthesis. Biochim Biophys Acta 726:149–185

Crofts AR, Baroli I, Kramer D, Taoka S (1993) Kinetics of electron

transfer between QA and QB in wild-type and herbicide-resistant

mutants of chlamydomonas-reinhardtii. Z Naturforsch C

48:259–266

Dau H (1994) Molecular mechanisms and quantitative models of

variable photosystem II fluorescence. Photochem Photobiol

60:1–23

Duysens LNM, Sweers HE (1963) Mechanism of the two photo-

chemical reactions in algae as studied by means of fluorescence.

In: Ashida J (ed) Studies of microalgae and photosynthetic

bacteria, Special issue of Plant Cell Physiol. University of Tokyo

Press, Tokyo, pp 353–372

Furbank RT, von Caemmerer S, Sheehy J, Edwards G (2009) C4 rice:

a challenge for plant phenomics. Funct Plant Biol 36:845–856

Govindjee (1995) 63 Years since Kautsky—Chlorophyll a fluores-

cence. Aust J Plant Physiol 22:131–160

Govindjee (2004) Chlorophyll a fluorescence: a bit of basics and

history. In: Papageorgiou GC, Govindjee (eds) Chlorophyll

a fluorescence: a signature of photosynthesis. Springer, Nether-

lands, pp 1–42

Govindjee, Amesz J, Fork DC (1986) Light emission by plants and

bacteria. Academic press, Orlando

Graan T, Ort DR (1984) Quantitation of the rapid electron donors to

P700, the functional plastoquinone pool, and the ratio of the

photosystems in spinach chloroplasts. J Biol Chem

259:14003–14010

Graan T, Ort DR (1986) Detection of oxygen-evolving photosystem-

II centers inactive in plastoquinone reduction. Biochim Biophys

Acta 852:320–330

Guenther JE, Melis A (1990) The physiological significance of

photosystem II heterogeneity in chloroplasts. Photosynth Res

23:105–109

Hall DO, Rao KK (1999) Photosynthesis, 6th edn. Cambridge

University press, Cambridge

Haumann M, Junge W (1994) The rates of proton uptake and

electron-transfer at the reducing side of photosystem-II in

thylakoids. FEBS Lett 347:45–50

Haveman J, Mathis P (1976) Flash-induced absorption changes of the

primary donor of photosystem II at 820 nm in chloroplasts

inhibited by low pH or tris-treatment. Biochim Biophys Acta

440:346–355

Holzwarth AR, Muller MG, Reus M, Nowaczyk M, Sander J, Rogner

M (2006) Kinetics and mechanism of electron transfer in intact

photosystem II and in the isolated reaction center: pheophytin is

the primary electron acceptor. Proc Natl Acad Sci USA

103:6895–6900

Joliot A, Joliot P (1964) Etude cinetique de la reaction photochimique

liberant l’oxygene au cours de la photosynthese. Comput Rend

Acad Sci Paris 258:4622–4625

Kautsky H, Appel W, Amann H (1960) Chlorophyll fluorescence and

carbon assimilation. Part XIII The fluorescence and the photo-

chemistry of plants. Biochem Zeit 332:277–292

Kok B, Forbush B, McGloin M (1970) Cooperation of charges in

photosynthetic O2 evolution I. A linear four step mechanism.

Photochem Photobiol 11:457–475

Krause GH, Weis E (1991) Chlorophyll fluorescence and photosyn-

thesis: the basics. Annu Rev Plant Physiol Plant Mol Biol

42:313–349

Kurreck J, Schodel R, Renger G (2000) Investigation of the

plastoquinone pool size and fluorescence quenching in thylakoid

membranes and photosystem II (PS II) membrane fragments.

Photosynth Res 63:171–182

Lavergne J (1982) Two types of primary acceptors in chloroplasts

photosystem-II.1. Different recombination properties. Photobio-

chem Photobiophys 3:257–271

Lavergne J, Briantais J-M (1996) Photosystem II heterogeneity. In:

Ort DR, Yocum CF (eds) Oxygenic photosynthesis: the light

reactions. Advances in photosynthesis and respiration, vol 4.

Springer, Dordrecht, pp 265–287

Lavergne J, Leci E (1993) Properties of inactive photosystem II

centers. Photosynth Res 35:323–343

Table 4 The definition of mathematical expressions used in the paper

Mathematical

expressions

Description

P ¼ PSII1; . . .; PSIINf g The PSII set P is constituted by N PSII units i.e. PSII1, PSII2, …, PSIIN

C ¼ OEC; Yz; . . .f g The electron transfer components set C is constituted by different electron transfer components i.e. OEC, Yz…S ¼ S1; . . .; Snf 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*}

PJ

j¼1

rj

Sum of rj, r2,.. rJ

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

Photosynth Res

123

Lavergne J, Trissl HW (1995) Theory of fluorescence induction in

photosystem II: derivation of analytical expressions in a model

including exciton-radical-pair equilibrium and restricted energy

transfer between photosynthetic units. Biophys J 68:2474–2492

Lavorel J (1973) Simulation par la methode de Monte Carlo, d’un

modele d’unites photosynthetiques connectees. Physiol Veg

11:681–720

Lavorel I (1986) A Monte Carlo method for the simulation of kinetic

models. Photosynth Res 9:273–283

Lavorel J, Joliot P (1972) A connected model of the photosynthetic

unit. Biophys J 12(7):815–831

Lazar D (1999) Chlorophyll a fluorescence induction. Biochim

Biophys Acta 1412:1–28

Lazar D (2003) Chlorophyll a fluorescence rise induced by high light

illumination of dark-adapted plant tissue studied by means of a

model of photosystem II and considering photosystem II

heterogeneity. J Theor Biol 220:469–503

Lazar D (2006) The polyphasic chlorophyll a fluorescence rise

measured under high intensity of exciting light. Funct Plant Biol

33:9–30

Lazar D (2009) Modelling of light-induced chlorophyll a fluorescence

rise (O-J-I-P transient) and changes in 820 nm-transmittance

signal of photosynthesis. Photosynthetica 47:483–498

Lazar D, Jablonsky J (2009) On the approaches applied in formulation

of a kinetic model of photosystem II: different approaches lead

to different simulations of the chlorophyll a fluorescence

transients. J Theor Biol 257:260–269

Lazar D, Pospısil P (1999) Mathematical simulation of chlorophyll

a fluorescence rise measured with 3-(30,40-dichlorophenyl)-1,1-

dimethylurea-treated barley leaves at room and high tempera-

tures. Eur Biophys J 28:468–477

Lazar D, Schansker G (2009) Models of chlorophyll a fluorescence

transients. In: Laisk A, Nedbal L, Govindjee (eds) Photosynthe-

sis in silico: understanding complexity from molecules to

ecosystems. Springer, Dordrecht, pp 85–123

Lazar D, Naus J, Matouskova M, Flasarova M (1997) Mathematical

modeling of changes in chlorophyll fluorescence induction

caused by herbicides. Pestic Biochem Physiol 57:200–210

Lebedeva GV, Belyaeva NE, Demin OV, Riznichenko GY, Rubin AB

(2002) Kinetic model of primary photosynthetic processes in

chloroplasts. Description of the fast phase of chlorophyll

fluorescence induction under different light intensities. Biophys-

ics 47:968–980

Leibl W, Breton J, Deprez J, Trissl HW (1989) Photoelectric study on

the kinetics of trapping and charge stabilization in oriented PS II

membranes. Photosynth Res 22:257–275

Maxwell K, Johnson GN (2000) Chlorophyll fluorescence—a

practical guide. J Exp Bot 51:659–668

Mccauley S, Melis A (1987) Quantitation of photosystem II activity

in spinach-chloroplasts - effect of artificial quinone acceptors.

Photochem Photobiol 46:543–550

Melis A (1985) Functional-properties of photosystem-II-Beta in

spinach-chloroplasts. Biochim Biophys Acta 808:334–342

Melis A (1991) Dynamics of photosynthetic membrane composition

and function. Biochim Biophys Acta 1058:87–106

Messinger J, Renger G (1993) Generation, oxidation by the oxidized

form of the tyrosine of polypeptide D2, and possible electronic

configuration of the redox State S0, S-1, and S-2 of the water oxidase

in isolated spinach thylakoids. Biochemistry 32:9379–9386

Munday JC Jr, Govindjee (1969) Light-induced changes in the

fluorescence yield of chlorophyll a in vivo: III. The dip and the

peak in the fluorescence transient of Chlorella pyrenoidosa.

Biophys J 9(1):1–21

Oettmeier W, Soll H-J (1983) Competition between plastoquinone

and 3-(3,4-dichlorophenyl)-1,1-dimethylurea at the acceptor side

of photosystem II. Biochim Biophys Acta 724:287–290

Papageorgiou GC, Govindjee (2004) Chlorophyll a fluorescence: a

signature of photosynthesis. Advances in photosynthesis and

respiration, vol 19. Springer, Dordrecht

Papageorgiou GC, Govindjee (2011) Photosystem II fluorescence:

slow changes—scaling from the past. J Photochem Photobiol

B-Biology 104:258–270

Rabinovich E, Govindjee (1969) Photosynthesis. Interscience Pub-

lishers Inc., Wiley, New York

Razeghifard MR, Klughammer C, Pace RJ (1997) Electron paramag-

netic resonance kinetic studies of the S states in spinach

thylakoids. Biochemistry 36:86–92

Renger G, Wolff C (1976) The existence of a high photochemical

turnover rate at the reaction centers of System II in Tris-washed

chloroplasts. Biochim Biophys Acta 423:610–614

Roelofs TA, Lee C-H, Holzwarth AR (1992) Global target analysis of

picosecond chlorophyll fluorescence kinetics from pea chloro-

plasts: a new approach to the characterization of the primary

processes in photosystem II a- and b-units. Biophys J

61:1147–1163

Rubin A, Riznichenko G (2009) Modeling of the primary processes in

a photosynthetic membrane. In: Laisk A, Nedbal L, Govindjee

(eds) Photosynthesis in silico: understanding complexity from

molecules to ecosystems. Springer, Dordrecht, pp 151–176

Sauer K (1975) Primary events and trapping of energy. In: Govindjee

(ed) Bioenergetics of photosynthesis. Academic Press, New

York, pp 115–181

Schansker G, Srivastava A, Strasser RJ, Govindjee (2003) Charac-

terization of the 820-nm transmission signal paralleling the

chlorophyll a fluorescence rise (OJIP) in pea leaves. Functi Plant

Biol 30:785–796

Schansker G, Toth SZ, Strasser RJ (2005) Methylviologen and

dibromothymoquinone treatments of pea leaves reveal the role of

photosystem I in the Chl a fluorescence rise OJIP. Biochim

Biophys Acta 1706:250–261

Schansker G, Toth SZ, Kovacs L, Holzwarth AR, Garab G (2011)

Evidence for a fluorescence yield change driven by a light-

induced conformational change within photosystem II during the

fast chlorophyll a fluorescence rise. Biochim Biophys Acta

1807:1032–1043

Schansker G, Toth SZ, Holzwarth AR, Garab G (2013) Chlorophyll

a fluorescence: beyond the limits of the Q model. Photosynth

Res. doi:10.1007/s11120-013-9806-5

Schatz GH, Brock H, Holzwarth AR (1988) Kinetic and energetic

model for the primary processes in photosystem II. Biophys J

54:397–405

Shevela D, Eaton-Rye JJ, Shen J-R, Govindjee (2012) Photosystem II

and the unique role of bicarbonate: a historical perspective.

Biochim Biophys Acta 1817:1134–1151

Stirbet A, Govindjee (2011) On the relation between the Kautsky

effect (chlorophyll a fluorescence induction) and Photosystem II:

basics and applications of the OJIP fluorescence transient.

J Photochem Photobiol B 104:236–257

Stirbet A, Govindjee (2012) Chlorophyll a fluorescence induction: a

personal perspective of the thermal phase, the J-I-P rise.

Photosynth Res 113:15–61

Stirbet A, Strasser RJ (1995) Numerical simulation of the fluores-

cence induction in plants. Archs Sci Geneve 48:41–60

Stirbet A, Govindjee, Strasser BJ, Strasser RJ (1998) Chlorophyll

a fluorescence induction in higher plants: modelling and

numerical simulation. J Theor Biol 193:131–151

Strasser RJ (1978) The grouping model of plant photosynthesis. In:

Akoyunoglou G (ed) Chloroplast development. Elsevier, North

Holland, pp 513–524

Strasser RJ (1981) The grouping model of plant photosynthesis:

heterogeneity of photosynthetic units in thylakoids. In: Akoyu-

noglou G (ed) Photosynthesis III. Structure and molecular

Photosynth Res

123

organisation of the photosynthetic apparatus. Balaban Interna-

tional Science Services, Philadelphia, pp 727–737

Strasser RJ, Govindjee (1992) The Fo and the O-J-I-P fluorescence

rise in higher plants and algae. In: Argyroudi-Akoyunoglou JH

(ed) Regulation of chloroplast biogenesis. Plenum Press,

New York, pp 423–426

Strasser RJ, Stirbet AD (1998) Heterogeneity of photosystem II

probed by the numerically simulated chlorophyll a fluorescence

rise (O-J-I-P). Math Comput Simul 48:3–9

Strasser RJ, Srivastava A, Govindjee (1995) Polyphasic chlorophyll

a fluorescence transient in plants and cyanobacteria. Photochem

Photobiol 61:32–42

Strasser RJ, Tsimilli-Michael M, Srivastava A (2004) Analysis of the

chlorophyll a fluorescence transient. In: Papageorgiou GC,

Govindjee (eds) Chlorophyll a fluorescence: a signature of

photosynthesis. Springer, Dordrecht, pp 321–362

Tomek P, Ilik P, Lazar D, Stroch M, Naus J (2003) On the

determination of QB-non-reducing photosystem II centers from

chlorophyll a fluorescence induction. Plant Sci 164(4):665–670

Toth SZ, Schansker G, Strasser RJ (2005) In intact leaves, the

maximum fluorescence level (FM) is independent of the redox

state of the plastoquinone pool: a DCMU-inhibition study.

Biochim Biophys Acta 1708:275–282

Toth SZ, Schansker G, Garab G, Strasser RJ (2007) Photosynthetic

electron transport activity in heat-treated barley leaves: the role

of internal alternative electron donors to photosystem II.

Biochim Biophys Acta 1767:295–305

Trebst A (1987) The three-dimensional structure of the herbicide

binding niche on the reaction center polypeptides of photosystem

II. Z Naturforsch 42c:742–750

Trebst A (2007) Inhibitors in the functional dissection of the

photosynthetic electron transport system. Photosynth Res 92:

217–224

Trebst A, Draber W (1986) Inhibitors of photosystem II and the

topology of the herbicide and QB-binding polypeptide in the

thylakoid membrane. Photosynth Res 10:381–392

Trissl H, Lavergne J (1995) Fluorescence induction from photosystem

II: analytical equations for the yields of photochemistry and

fluorescence derived from analysis of a model including exciton-

radical pair equilibrium and restricted energy transfer between

photosynthetic units. Aust J Plant Physiol 22:183–193

Van Grondelle R (1985) Excitation energy transfer, trapping and

annihilation in photosynthetic systems. Biochim Biophys Acta

811:147–195

Velthuys BR (1981) Electron-dependent competition between plas-

toquinone and inhibitors for binding to photosystem-II. FEBS

Lett 126:277–281

Velthuys BR, Amesz J (1974) Charge accumulation at the reducing

side of system 2 of photosynthesis. Biochim Biophys Acta

333:85–94

Vernotte C, Etienne AL, Briantais JM (1979) Quenching of the

system II chlorophyll fluorescence by the plastoquinone pool.

Biochim Biophys Acta 545:519–527

Whitmarsh J, Ort DR (1984) Stoichiometries of electron-transport

complexes in spinach-chloroplasts. Arch Biochem Biophys

231:378–389

Yang J, Monine MI, Faeder JR, Hlavacek WS (2008) Kinetic Monte

Carlo method for rule-based modeling of biochemical networks.

Phys Rev E Stat Nonlin Soft Mat Phys 78:031910–031917

Zhu XG, Govindjee, Baker NR, DeSturler E, Ort DR, Long SP (2005)

Chlorophyll a fluorescence induction kinetics in leaves predicted

from a model describing each discrete step of excitation energy

and electron transfer associated with photosystem II. Planta

223:114–133

Photosynth Res

123