Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://library.biophys.msu.ru/PDF/3341.pdf Äàòà èçìåíåíèÿ: Mon Mar 17 13:28:12 2008 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 19:39:06 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: m 67

Biophysics, Vol. 47, No.6, 2002, !lp. 968-980. Translatedfrom Biojizika, Vol. 47, No.6, 2002, pp. 1044-1058. Ori/ibwf Ruxsiun Text Copyri/ihl Cd 2002 hy Lrhedcvu, BdY(l('lIu, Demin; Rimichcnko, Rubin. El!l!li.l'h Translution Cllpyri/ihl (c) 2002 liy MA1K "Nauta/lnterperiodica" tRuxsiu].

CELL BIOPHYSICS

Kinetic Model of Primary Photosynthetic Processes in Chloroplasts. Description of the Fast Phase of Chlorophyll Fluorescence Induction under Different Light Intensities
G. V. Lebedeva-, N. E. Belyaeva", O. V. Demin-, G. Yu. Riznichenko", and A. B. Rubin
J Biological Faculty, Moscow State University, Moscow. 119899 Russia 2Be/ozersky Institute of Physico-Chemical Biology, Moscow State University, Moscow, J] 9899 Russia

l

Received September 2,2002

Abstract-s-A kinetic model was developed for generation and utilization of the transmembrane electrochemical proton gradient in primary photosynthetic processes in chloroplasts. The model gives a detailed description of the catalytic cycles in photosysterns J and II, the cytochrome b,:t"cornplcx, ATP synthesis, and passive leakage of H+, K+, and CI- through the thylakoid membrane. Account is taken of the dependence of the electron transport rate on the transmembrane potential. The model was tested for consistency with the experimental data on the fast phase of chlorophyll fluorescence induction under different light intensities (high to low). The composition of the fluorescence response was analyzed for each illumination level. Key words: regulation, photosynthesis, mathematical model, fluorescence induction

INTRODUCTION The information conveyed by chlorophyll fluorescence is commonly used to study the state of the plant photosynthetic apparatus [1--4]. In this regard, one of the most important effects is fluorescence induction, i.e., the change in the intensity of the fluorescence of a dark-adapted specimen developing upon exposure (0 constant illumination, This phenomenon was first reported in 1931 [5] and actively studied later [1-3, 6-8]. The induction curves thus registered reflect the process of plant adaptation to new illumination conditions, and are multiphasic (see inset in Fig. I) because the photosynthetic system comprises processes with different characteristic times. At present, it is generally accepted to consider the following main phases and parameters of chlorophyll fluorescence induction: fast phase, whereby the fluorescence intensity rises from the initial level F o tu the maximal F; within a time on the order of seconds; and slow

phase, whereby the fluorescence intensity certain steady state F T within some tens The pattern of the fast phase depends on tensity. Under low illumination there is intermediate phase J, whereas under high there are at least two, J and 1.

relaxes to a of seconds. the light inusually one illumination

In general, the fluorescence induction curve is
an overall result of interaction of the processes of energy transduction and electron transfer along the photosynthetic chain. One can qualitatively collate separate components of the induction curve with particular processes that take place in the plant photosynthetic machinery (charge separation in the reaction
center, generation of the transmembrane electrochem-

ical proton potential, changes in the redox state of the plastoquinone pool, etc.). Indeed, all these processes
arc interconnected, and it is often hard 10 determine

Abbreviations: Chi, chlorophyll; Fd. ferredoxin; Pc, plastocyanin; Phc. pheophytin; PQ, plastoquinone; PQH:, or QH:" plastoquinol: PS. photosvsrem: WSC water-splitting comnlex.

what contribution is made by each of them to the phasing of the induction curve. To interpret the experimental results, use is commonly made of the methods of mathematical modeling, permitting assessment of the photosynthetic processes that give rise to the induction effects [9-171, The notions on the mechanisms of


KINETIC MODEL OF PRIMARY PHOTOSYNTHETIC PROCESSES

969

2H+

F
p
/.1

Lumen
"-

J ....i

0/'
.....

...r

Tbylakoid

membrane Stroma

(
,-J.-""- ATP

ATP synthase

Fig. 1. Flowchart for the generalized model of primary photosynthetic processes. PS. photosysrcm: ChI, antenna chlorophyll. P680 and P700, pigments of the PS II and PS I reaction centers; FeS" acceptor complex of PS I; Fd, ferredoxin; Pc, ptastocyanin; bf, cytochrome hlf complex, b h and hi, high- and low-potential hemes: FeSR. Rieske iron-sulfur center; R-COO- designate buffer groups. Signs (+) and (-) on the membrane indicate that the rhylakoid lumen is charged positively and the chloroplast stroma is charged negatively in the course of the photosynthetic processes. Solid zigzag arrows denote quanta of incident light and Iluoresccnce/ Common arrows indicate the direction of electron transfer along the chain and the ion fluxes across the thylakoid membrane upon the onset of illumination. Thc inset schematically depicts the chlorophyll fluorescence induction curve with conventional phase designations: upward aITOW at the abscissa axis marks light on.

photosynthetic processes laid into such models inevitably influence the interpretation of results obtained upon fitting the model parameters to the experimental data on chlorophyll fluorescence. The simplifications introduced in most of the models describing the fast phase of the induction curve make them applicable only to certain 'particular cases' of experimental fluorescence curves. Thus chlorophyll fluorescence induction was assessed in the presence of an electron transfer inhibitor diurcn, when the induction curve lacked intermediate phases. Some models [10-12] describe the fast phase under low illumination; other models [13, 19] ",'ere proposed for the same process under intense illumination. Further, most of the models available are restricted to the processes in photosystem 11. inasmuch as its chlorophyll makes the major contribution to the fluorescence under study. However, any such model thereby neglects other processes that can influence the parameters of primary photoreactions, in particular,
BIOI'HYSICS

generation of the transmembrane proton gradient ,1.!J. H· with participation of the PS 1 complexes and cytochrome b/f complex, as well as processes dissipating L'l.!J.w such as ATP synthesis and passive leakage of H+, K+, and Cl- ions. We propose a generalized model of primary photosynthetic processes, integrating the main modern notions on the structure and function of the photosynthetic machinery of green plants. Separate aspects of the model have been discussed elsewhere [20-24]. In the framework of the model, we present a description of the fast phase of chlorophyll fluorescence induction as dependent on the kinetics of the main primary steps of photosynthesis in a broad range of illumination intensity. DESCRIPTION OF THE MODEL Our model of primary photosynthetic processes is compartmentalized, and describes the events taking place in the three main compartments of the

Vul -17

reo. h

2UU2


970

LEBEDEV A et at.

chloroplast: stroma, thylakoid membrane, and thylakoid lumen. The general scheme of the processes thus considered is given in Fig. 1. Illumination initiates electron transfer along the electron transport chain with coupled transmembrane proton translocation from the chloroplast stroma into the thylakoid lumen, whereby an electrochemical proton gradient ~/lw (with electric and concentration components ~'fI and cpl-l) is created across the thylakoid membrane. Generation of 6./l w involves highly specialized pigment-protein complexes of photosystems 1 and 11 as well as the cytochrome b/f complex. The 6.).lw is utilized in ATP synthesis by ATP synthase, and is also spent in R.., K+, and Cl- leakage through the energized thylakoid membrane and in drawing electrons off PS I through the ferredoxin:NADPH reductase reaction. The model is kinetic, being a set of ordinary differential equations that for every moment of time determines the state of the system of chemical reactions under study, i.e., gives the concentrations of the metabolites of the aggregate of reactions as functions of time. These balance equations are written as

by the overall concentration of the given complex in the system. Electron transfer from a pigment-protein complex to a mobile carrier was described by acting mass equations with bimolecular rate constants, taking the complex concentration to be equal to the sum concentration of its states capable of participating in the given electron transfer step. In our model, the reaction rates are functions of variables involved in the given step as well as functions of model parameters. Evaluating the parameters of each reaction, account was taken of the relation between the rate constant of the forward and reverse reactions through the equilibrium constant:
(2)

The equilibrium constants of redox reactions were determined from the experimental data on midpoint redox potentials:
K
eq

= exp

( !>.Em / ' lRT nF)

I

(3)

.z:s:
dt

dX

=Vprd(Xi)-Vcl1,(Xi),

(1)

where Xi is the concentration of the ith metabolite in mM, l'prd(X,) and vcns(X,) are the overall rates of its production and consumption, mM/s. The photosynthetic electron transport chain includes mobile carriers (plastoquinone PQ, plastocyanin Pc, ferredoxin Fd) as well as carriers grouped in pigment-protein complexes of PS I, II, and blf. It is known that acting mass equations are inapplicable to describing electron transfer between carriers within an integral complex [25-27]. Therefore, to consider the processes within the PS I, II, and blf complexes, we resorted to an approach based on detailed description of the catalytic cycles for each such complex. The latter was described as a set of possible states, the number of which is determined by the number of electron carriers entering into the composition of the complex and the number of possible redox states of each carrier (e.g., excited, oxidized, reduced). Type (1) equations were written down for every possible stale of the complex, with the variables Xi meaning the probability of the ith state of complex multiplied

where 6.E m is the difference of midpoint redox potentials measured relative to a standard hydrogen electrode, and n is the number of electrons transferred in the course of the redox reaction. The I:1E m values were taken from the literature [28-31]. The equilibrium constant values calculated with equation (3) were used only as preliminary estimates, because the 1:1¸", for a redox pair is usually measured under special conditions far from those in vivo. Therefore, some K eq had then to be changed to improve the fit between the calculated and experimental data on fluorescence induction.

Dependence of Reaction Rate on Transmembrane Electric Potential
Any reaction step involving electric charge transfer across a membrane produces a transmembrane electric potential L1'f1, which, in its turn, influences the rate of electron transfer along the electron carrier chain [32-34]. The model takes this into account as the corresponding dependences of equilibrium and rate constants on 1:11.1' as follows:
K
eq

( L1 lf' ) = exp(-Mlf' / (RT /

F))K

cq ,

L(t.'P) = exp(~oat.'P /(RT /

F))k ..

Ut.q')= exp(1 ~o)at.q' /(RT / F))L
LllOI'HYSICS V(1I, -17 "'(1, ()
~()U::


KINETIC MODEL OF PRIMARY PHOTOSYNTHETIC PROCESSES

971

Here a is the portion of l.l.\V that is generated at the particular step by charge transfer across the membrane; 8 is the portion of the membrane potential M\jI that affects the rate of the direct reaction; Keq, k+, and k; are the corresponding constants at Ll'V ::: O. The electric membrane potential .6.", is a model variable, its time dependence is described by a differential equation
F~ =v qlumcn -v(qstroma'
Cm

reduction of plastoquinone to plastoquinol and creates a transmembrane electrochemical proton potential .6.!lw (Fig. 2). A detailed description of the PS IT model has been given elsewhere [23J. Every kinetic state of PS II is determined by the states of its four constituent electron carriers: chlorophyll P680, pheophytin Phe, primary one-electron covalently bound quinone acceptor QA' and binding site for the secondary quinone acceptor OIl' It is assumed that the excitation energy initially localized on one of the antenna pigments is rapidly (within picoseconds) equilibrated over the entire pool of PS II antenna pigments including the P680 reaction center pigment [2, 3, 41]. Therefore, the designation Chi covers the whole complex of these pigments. Kinetic states Xi, Yi' Z;, gj (i::; the state of the QB binding site: in in Xi the site contains nonreduced PQ in the site carries one (OB) (O~-), respectively. 1,2, ... -7) differ in gi the site is vacant, Qa, in Yi and t, the and two electrons

d(ll'!')

()

)

where em is the specific capacitance of the thylakoid membrane, F is the Faraday constant, and v(q) are the rates of charge bulk density production, measured in mM and dependent on H+, K+, and Cl" concentrations in the respective compartments. The concentration component (.6.pH) of the proton electrochemical potential is also a model variable, determined at every moment by the difference in proton concentrations in the stroma and in the lumen. Buffer Properties of Lumen and Stroma The chloroplast stroma and the thylakoid lumen are known to exhibit buffer properties owing to the presence of various proton-binding groups in their volume. In our model, we approximate the buffering in these compartments with three proton-binding groups (B l , B2 , B3) , their pK for protons varying from 4 to 8. The dissociation constants and the concentrations of buffering groups were chosen so as to fit the experimental data on the buffer capacity of the thylakoid lumen [35]. Consumption of the Transmembrane Electrochemical Potential .6.!lIJ+ In our model, the .6.J.l-w is utilized in ATP synthesis by ATP synthase, and is also spent in passive leakage of H+, K+, and Cl through the thylakoid membrane. The rate equation for the ATP synthase reaction is based on the minimal kinetic scheme of ATP synthesis/hydrolysis [34, 36, 37]. The dependence of proton leakage on the potential has been obtained [36, 38--40] within the framework of Eyring's model of ion transport through a three-barrier channel. The same mechanism was used to describe the electrogenic transmembrane transport of Cl" and K+. Photosystem II In our model, PS II is regarded as a membrane enzyme that under the action of light catalyzes
BIOPHYSICS Vol.47 No.
(1

Without illumination (dark adaptation) the PS II complex acquires states Xl and gl' which come into equilibrium (step 34). When the light is switched on, P680 goes into excited state (steps 1 and 28), which may be accompanied by primary (steps 2 and 29) and secondary (steps 3 and 30) charge separation. The wator-splitting complex reduces the oxidized reaction center pigment (steps 4 and 3 J). We did not consider the molecular mechanism of the WSC operation, but assumed that per every electron passed from WSC to oxidized P680 there is one proton released into the intrathylakoid space. Thus, the sequence of steps 1---4 or 28-31 results in formation of "closed" reaction centers with reduced QA (states Xj and gj). Further illumination of closed RC may repeated excitation of the pigment (steps 5 and primary charge separation (steps 6 Thereby arise the PS II states with oxidized and reduced Phe and QA (states X7 and g7)' result in and 32) and 33). pigment

In any state gi (i ::: I, 7), PQ can bind in the QI:l site (steps 34---40) to give the corresponding states Xi (i = I, ... 7). The bound Q8 is a two-electron carrier and can consecutively accept two electrons from OA' Steps 7 and 14 describe the transfer of the first and the second electron to QB with formation of states Yl and '::1' Under light, these states can undergo the sequence of conversion described for Xl and gl' including pigment excitation (steps 8 and 15), primary

.:'(I(J.:'


972

LEBEDEVA et at.
--- -------.- ---"--. :7

::1

Chi
Pile

Qi
01
a

QA

PQH

15

------~

16

Qi

Chi Phe QA

17

.---

------~

Chi Phe -'~---~ QA - >18

Chi Phe QA-

-

Q~ 2H ; 23

Q~

2

19

20
>

~12H;
l 2

j PQH 2 K3

~

W "4
Ch1+ I'he

2H;
III --,"- __..

24 PQH']

Chi

Phe

QA

28
PQ
4

ChI + _ Ph,

+

N
Chi Phe

t: 2H: l..25

7PQH g,

30

QA
f1;.PQ

5

32

33

CI1I+ Phe -

QA

W x,
ChI

j x,
1

36
7

Ph'

QA QB

7
Y3

3

Chi Phc

QA-

QB

..

·

Chl Ph' QA QB

·....................................

· )'1
Chi

)'4

)'5

Phe QA

.s,
..

Chl+ Phe

10 ...

Chl +
Phe

H+

_~

--,"- ..~

I

ChI

Phe

QA
QB

QB

QA - · 11 QB -

QAQB-

,........

·,

-

-ll

Fig. 2. The catalytic cycle of photosystem II. Each rectangle represents a particular kinetic stale determined by rhc redox slate of i ts constituent electron carriers. Shaded arc the suucs capahlc of emitting fluorescence quanta. Chl. the total PS fl chlorophyll ineluding the antenna and the P680 pigments; Phe. pheophytin; QA and QH' primary and secondary quinone acceptors; I'Q, plastoquinone; PQH;" plasroquinol; H! and Hi are protons released into the lumen and taken up from the stroma, respectively. Dotted arrows denote the fast steps (charactcri sue time less than 0.1 ms), continuous arrows denote the slow steps (characteristic time nr least I ms). bold arrows mark the light steps. Numbers lit the arrows and designations utthe tops of the boxes correspond [0 the step numbers and model variables.

(steps 9 and 16) and secondary (steps 10 and 17) charge separation, reduction of oxidized P680 by WSC (steps 11 and 18), and excitation of closed RC (steps 12 and 19) attended by primary charge separation (steps 13 and 20). In any state :::i (i::: I, ... 7), plastoquinol PQH 2 may be released (after uptake of two protons H~) from the chloroplast stroma, giving states gi (i::: 1, 7) with vacant QB site (steps 21-27), and this closes the catalytic cycle of PS II.

Steps 1,5,8,12,15,19,28, and 32 marked with bold arrows in the scheme are the light steps, describing the transition of ChI into the excited state Chl'' (light constant kL ::: i, where i::: 1, 5, 8, 12, 15, 19,28, 32) and the reverse process of deactivation of the excited state with emission of fluorescence quanta (flue.rescence constant kF = k.. , where i ::: I, S, 8, 12, 15, 19, 28, 32). To calculate and compare the fluorescence yields under different light intensities, we used the function F presented as a sum concentration of PS II


KINETIC MODEL OF PRIMARY PHOTOSYNTHETIC PROCESSES

973

(3)

~'-Q:\
I FeS i HI

!

I

bi]

67~
bI

... per
~Pcox

Fig. 3. The catalytic cycle 01' the cytochrome hI,(complex. Each rectangle represents a particular kinetic state determined by the redox stale of its constituent electron carriers. Superscripts mark the reduced (r) and oxidized (ox) states. Designations in ovals correspond to the model variables.

fluorescing states (i.e., states with excited Chl*) multiplied by the ratio of fluorescence and light constants:

Cytochrome blf Complex The cytochrome b/f complex was regarded as a membrane enzyme catalyzing electron transfer from plastoquinol to plastocyanin coupled with proton transport from the stroma into the thylakoid lumen. The corresponding aggregate of redox reactions IS known as the Q cycle and 'is presented in Fig. 3.
The b/f complex has two catalytic centers-luminal (p) and stromal (n)-involved in the redox conversions of PQ [29]. In our model, the electrons are fed into the Q cycle (bold arrow without number in Fig. 3) via the reaction of Q reduction to QH 2 by PS LL (steps 21-27 in Fig. 2). This process takes place at the stromal (s) surface of the thylakoid membrane, after which plastoquinol diffuses to the luminal (I) side of the membrane (step 41, dotted
BIOI'HYSICS V"I -'17

arrow in the left-hand part of Fig. 3). Upon binding with the (p) center of the bIJ complex, the pJastoquinol passes one electron to the Rieske iron-sulfur center (FeS) and releases one proton into the thylakoid lumen; this makes a complex of protonated PQ with reduced FeS (steps 43, 44, 45, 46 depending on the redox states of FeS and the cyt h hemes). 1f the low-potential heme of cyr b is reduced, the semiquinone remains bound at the Rieske center until b l is oxidized (in steps 49, 55, and 61). Then the second proton is released, and the semiquinone of the FeSr-QH· complex gives the electron to the b l heme, thus converting into free PQ (steps 47 and 48), and diffuses back to the stromal side (step 42, dotted arrow in the upper part of the scheme). Further, the electron is transferred across the membrane from the low-potential to the high-potential heme (steps 61---63). Thereupon the reduced hh heme reduces the PQ in the (n) center to produce semiquinone Q~ (steps 49-54). This semiquinone takes the second electron from h), to become a plastoquinol through consuming two protons from the stroma (steps 55-(0). Simultaneously, the electron accepted by the FeS center is transferred

x..

r.

::'Oli::'


974

LEBEDEVA et at.

(PSI 4)

FdJ'

..;:~/

<: -:»:

7~/' ~/"
68

t/.
Fd
QX

P700

FeST

'" ~ ~.~
".'" "
.

Pcox

.~ "
~

Per

(PSI 2)

'>.- ..... '

P700 (PSI,)
FeSo'

·

·

1'700~

FcS

oX

·

G9

·

1'700+
FeSt'
(PSI])

1'700+

FeS ox
(PSIs)
Fig. 4. Electron transfer in photosyster» I. P70() is the reaction center chlorophyll, FeS here means Ihc entire acceptor complex; Fd. ferredoxin: Pc, plastocyanin; superscripts mark the reduced (r) and oxidized (ox) states. (PSI,) correspond 1O the model variabies.

to cytfand then to Pc (steps 64-(7). The scheme does

nor show the step corresponding to electron transfer between Fe Sand cyt i. because these carriers are in fast equilibrium (both rate constants >10-'; S-I, equilib-

rium constant about 3 [29]). We assumed that the Q cycle has tour electrogenic steps: the first one corresponds to transmembrane electron transfer from blto b h (61-63), and the other three correspond to proton transport in plastoquinone reduction (55-60) and plasroquinol oxidation (43--48). The intcrheme electron transfer was taken to be responsible for 80 0!o of the overall electrogenesis, and the remaining 20% were shared equally between the proton-transport steps, which is in accord with the data [42, 43J obtained for the cytochrome bel complex of purple bacteria.
Photosystem I Vv'e regarded PS I as a membrane enzyme that under the action of light catalyzes oxidation of plastocyanin and reduction of ferredoxin. The scheme of the PS I catalytic cycle is given in Fig. 4" In our model we considered five possible kinetic states of PS 1, which are determined by the state of the P700 reaction center pigment and the FeS acceptor complex. Note that FeS here designates the entire complex of

acceptors: primary and secondary Ao and AI as well as the iron-sulfur clusters F~, FA. and F B . We did not go into details of electron transfer within the FeS complex, but assumed that the latter can be in two states, oxidized and reduced. This simplification appears expedient, because the electron transfer along the Ao-AI-r, chain is very rapid (10- 12 to 10'-9 s) [30]. Again, PS I comprises only one-electron carriers, which implies a simpler kinetic behavior of the system as compared with PS II. Onder light, the P700 passes into excited state P700* (step 68), with subsequent charge separation (step 69) and formation of state P700+FeS r. This state can further be "utilized' in two ways. Oxidized P700~ may first accept an electron from Pc (step 70), after which the acceptor complex will reduce Fd (step 7]); or vice versa, first the reduced FeS complex may give its electron to Fd (step 72) and then Pc will reduce the oxidized P700 (step 73). Table I lists the values for the model parameters. Estimation of the rate constants is a separate problem. Some values can be determined accurately enough (for instance, the rate constants for charge separation in PS 11) owing to the vast experimental material accumulated. Other processes are less studied, and the literature data on their parameters are
IllOl'HYSICS
VllI,~"

x.,

t,

xn:


KINETIC MODEL OF PRIMARY PHOTOSYNTHETIC PROCESSES Table 1. Model parametersDirect reaction rate constant (S-I)
kl=b,=ks""k 1Z""

975

Reverse reaction rate constant (k, stant (K)
=
k_ 19

5- 1)

or equilibrium con-

=kI5=kI9=k28=kn k k9""'k I6"" k

15; 150; 1500 depending on illumination 3.3.101
1

k_l= L 5= k_8= k_1 k_I. = 1 2=

=

k_ 2S=

k_32
2000

2=

29

K] = K y = K 16= K 29

k:1""kJO=kI7=k30
k4=kll=kIS=k31

5· lO9
5000
3.3.10
11

K 3 = KI(I= KJ7=

K~o

10' 100
200

K4 = K 11= K IS= K 3l

k6""k n=k 10=k"J

K6 = K"

k, k"
k
2 1 ""

2500/4348 2174
"'"

K,
K"
K11=Kn=K23=K24= = K 25= K 26= K 27 K:J = K" = K"6 = K,,= 4 = K3S = Kw = K4{)

20 10
5

kn = ky>, = k Z4 = k2 5 = k26 = k27

SOD
100 25 25

k]4=k35=kJG=k37= = k~8= k w = k 40
k
4l

k"
k4J = k 44 = k45= k46 k47 = k4~ k49=ksl=k53 kso=ks2=k54

500 2.10 200
100 25
5

K4:1 = K« = K45 = K 46 K47 = K 48 K 49= K SI = K 53 K50=Ks2=Ks4 K"

24
10 2.5 2.5 400 100 10

=

K SfJ

= K S7= K S8= =K'9=KG O
K6(, == KG 7

14,1 = k 62 = k G 3
kM

10'
2000

K61= K 62= K G 3 K(,4

=

k G = k66 = kG 5 7 k 68

=K G ::= ,

7.5; 75; 750 depending on illumination

k-0 8

105

k,"
k
70

K,"
K
70

104

= k73

=

K7~

100

k7 1=kn
'" Constant> numbered as the reaction steps in Figs. 2-4.

K

i l ::=

Kn

1000

contradictory. This particularly regards the slower processes such as PQ diffusion in the thylakoid membrane as well as transmembrane ion transport and the buffer properties of lumen and stroma. In this connection, most of the equilibrium and rate constants for the reactions considered in the model were averaged from the literature. At the same time, some parameters were optimized so as to attain a satisfactory fit to the experimental results.
BIOPHYSICS \"11. -1-7
,'\'Ll. ()

RESULTS

The data below were obtained by solving numerically the set of model equations using the SCAMP package in a Pentium-If Pc. The model of primary photosynthetic processes in plant chloroplasts was used to calculate the theoretical curves of chlorophyll fluorescence induction at different light intensities. The latter were set with

21l0:


976

LEBEDEV A et at.
co;;

Table 2. Stationary values of model variables for the dark-adapted object (k,

O. 1 = I. 5, ii. 12, IS, 19, 21), 32) 3.24
lO 10-4·1

x,
xi' i
co;;

1.34 0.0
0.28

PcO>

2, ... 8

He
W,

g,

(pH7.1)

)'" i = I, .8
r.. i = l , ... 8

0.0 0.0
1.62

Ke
K/

120 30
lO

[1'1=1., .. 12; i:;/: 5 PSI PSI
i, I

"

o.Cl
s

0.0
1.62

30 0.0 8.0

Fd' Fdo,

i= 2, ... 5

0.0
4,86 4.86

PQ, PQ, PQH2J PQH Pc'
2,

ATP ADP
P,

05
9.5 40 1.0 0.0

0.0 0.0 0.0

NADP NADPH

appropriate values of light constants ki (i = 1, 5, 8, 12, 15, 19, 28, 32, 68) and corresponded to 15, 150, or 1500 quanta per second per PS 11 reaction center. The relative fluorescence yield at every moment after the onset of illumination was calculated according to equation (4). To model the changes in the state of the photosynthetic system after switching on the light, we had to choose the initial values of the variables that would correspond to the 'dark' state of the object. To this end, the stationary solution for the system was obtained in the case when all light constants were zero, and the resulting set of values was taken as the initial in all further calculations (Table 2). The data listed in Table 2 pertain to average chloroplast velume 40 ~m3; P700 content 2 mmol per 1 mol chlorophyll; and chloroplast stroma, thylakoid lumen, and thylakoid membrane volume ratio 10: 1: 1. The stoichiometry of PS TI, b/f, PS I complexes, PQ, and Pc in the thylakoid membrane was taken to be J: I: I :6:2. As evident from Fig. 5, the model provides a good fit to the available experimental datil on fluorescence induction under different illumination conditions. AI small values of the light constants corresponding to low illumination (I %), fluorescence reaches its maximum in about 1-2 s, and the induction curve exhibits one intermediate phase (shoulder) at about 200 ms. A tenfold increase of the light constants, corresponding to medium illumination (lO%),

brings about a rise in the signal amplitude and shortens the time to the maximum (about 500 ms); the intermediate phase is less pronounced. At high light constants (intense illumination, 100%) fluorescence reaches its peak in 100-200 ms, with two intermediate phases (J about 2 ms and I about 20 ms). To elucidate the nature of individual kinetic components of the initial part of the induction curve, we plotted the time dependences of the concentrations of PS II states capable of emitting fluorescence quanta (the 2nd and the 6th forms shaded in Fig. 2), Modeling revealed that at any light intensity the contribution of the states with oxidized QA (2nd forms) to the fluorescence is several orders of magnitude smaller than the contribution of the states with reduced QA (6th forms). This is in accord with the existing notion that overall fluorescence is proportional to the concentration of closed (i.e., Q;;. -containing) reaction centers of PS II [13]. For this reason, in further analysis of the fluorescence induction curves we can restrict ourselves to considering the kinetics of the PS II fluorescing states with reduced QA (xt>, gel' Y6' '::6)' As demonstrated in Fig. 6b, the relative contribution of each fluorescing form depends on the light intensity. Thus under 10\\,' illumination fluorescence is mostly emitted by states gb (the quinone acceptor with reduced QA and vacant QlJ) and '::6 (Q;;'Q~-). Indeed, these states are generated in the light from g~ and z~ which do not allow electron transfer from QA along
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KINETIC MODEL OF PRIMARY PHOTOSYNTHETIC PROCESSES

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the chain (secondary acceptor either absent or fully reduced). As PQ attachment to the QB site and PQH 2 dissociation therefrom are relatively slow processes, states g'i and :'i (and hence g6 and Z6) can accumulate to greater concentrations than the corresponding x and y, in which the secondary acceptor is not fully reduced and the Q;;. electron can be transferred to QIl to yield respectively}'] and ':1' When the light is weak, this process prevails over formation of the excited slates, so that fluorescing forms X6 and Y6 are minor. Linder moderate illumination, the fluorescence of the system is also largely determined by the sum of g6 and Z6, though the fraction of X(, and )'6 increases somewhat. Under intense illumination, the contribution of X6 and )'6 to the fluorescence is comparable to that of g6 and Z6, because the characteristic time of the formation of the excited states becomes close to the time of electron transfer from QA to QR' The fluorescence induction curve exhibits two distinct intermediate phases J and 1; the former is provided by X6 and )'6 and the latter is provided largely by Z6' while g6 contributes to both. The analysis of the kinetic components of the fluorescence induction curve allows some conclusions concerning the origin of its phases J, 1, and P. The fluorescence peak P corresponds in time to attaining the maximal sum concentration of PS 11 fluorescing states with "fully closed' quinone acceptor complex C!i6 and Z6)' Phase 1 is quite distinct at any illumination intensity, and the time to this phase shortens with increasing light intensity. As can be seen in Figs. 6a and 6b, the onset of this phase roughly corresponds 10 the appearance of an intermediate maximum on the curve for the 7.(, content. Phase J is clearly discerned only under intense enough light, and is associated with accumulation of fluorescing states in which the acceptor is not fully reduced (not more than one electron on

5

(a)

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P

I

, "

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0

u

oS

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Fig. 5. Chlorophyll fluorescence induction curves at different light intensities. (a) Experimental data obtained upon illumination of dark-adapted pea leaves with red (650 nm) light at (lOO'i1r-) 600, (10%) 60, and (1%) 6 W/m 2 ; cited from [44]. (b) Calculations with the proposed model for illumination at (100%) 1000, (10%) 100, and (I %) lOW1m2 , setting the PS II light constants to 1500,150, and 15 s-'.

peak concentration change with the frequency at which the light quanta get into the reaction center. Of special interest are the causes of nonmonotone behavior of the z(, content, which gives rise to the I phase on the induction curve. Noteworthy is the correlation of the additional z(, maximum with the 'second wave' of the transmembrane electric potential A\j1; this is most clearly seen at low values of the light constants (Fig. 6a). The literature reports experiments QJl registering what IS known as the "slow phase of electrochromic changes" in the absorption of light by carotenoids (whose spectrum is sensitive to electric field) upon illuminating the object with a train of flashes. The observed 'slow' 00-20 ms) changes in pigment absorption reflecting the A\V shift are conventionally attributed to electrogenic electron transfer beyond the photochemical reaction centers of PS II. Thus considered were the roles of the bit" complex [29, 45, 46], of PQ and the FeS center [47J, and of PS I [48J in emergence of the slow phase. The slow phase of electrochromic changes

Q,).
Collation of the modeling results for different light intensities leads to a conclusion that under all conditions the induction curve features all kinetic components, but they are pronounced to a varying extent and appear at varying times. Indeed, the overall fluorescence at every moment is determined by the sum of fluorescent signals emitted by different redox states of PS II (eight in our model), and all these states are present in the system under any illumination, but the fractions of each state and the time to
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F tg. 6 . Ind u c tio n effe ct s calculated w ith the propose d mod e l for thr e e ill um in ati on le vel specified al the to p of each col u mn. The t ime scale is lo g arithm ic . Pa nel s (a), re l at ive flu or esc en ce y ie ld (F) an d trans mem bran e e lectric poten tial (8 0/). Pa ne l s (b ), con ce ntrat io ns o f PS II e xc ite d stares . Pan e ls (e ) rate s of pro c e sse s p r odu ci n g an d c o ns um in g t he elec tric charge in th e thyla ko id lumen : Hi:,. is the p ro to n in flu x fr om pla stoqui no l oxid a tio n at th e cy t blf lum i nal side, H ~ ~ is the pr oton influx from the water -splining co mpl ex; H1TP is proton co ns umptio n in t he AT P syn thase r ea cti on : K t.u is K+ leakage th roug h the me mbrane .

w as rep ort ed to be esp e cially distin ct at low light inten sity [4 9]. In term s of our mode l, .1.'1' at every momen t is d etermin ed by t he charge differenc e betwe en lumen and st ro ma. Figure 6 c dep ict s the time chan ges in the rat e s of proc e s se s involved in generation a nd ut iliz at ion o f e lect ric c ha rge in the lume n . Focu sing on the lef t-hand pa ne l s of Fig. 6 , on e c a n see t hat e me rgence of the Do'l' 's lo w pha se ' co inc id es with the e stab lishment o f a ce rt a in q uasi-stead y sta te of the cha rgeprod uc in g sys te m of t he t hy la koid lumen . The latter mean s that o ver the per iod from ca . 50 to ca. 30 0 ms the op pos ite ly dir e cted process e s largel y co un terbal a nce each ot her. From 5 0 to 200 ms, t he proton influx to the lum en i nc re a se s owin g to plastoqu inol ox idation at the lumi nal side of the b/f c o mplex (Fig . 6 c , H ~ . ) , a s t he s ys te m accum ulate s state s with Q ~ wh ich upon p rotonati on di ssociat e s from PS II, and

ac cum ulati on o f pl asroquin ol at the st romal side of the thylak oid membrane 's ta rts' the hi! compl e x. Th e pro to n influx fr om the wa ter - spl ittin g co mplex ( H ;;"'sd and b/fi s balanced by the K + leaka ge ( K:ead) and prot on co nsu mpt io n in the ATP syn t hase reacti on ( H tT p) . Be side s, a f ract io n of proton s i s tak en up by the buffe r (not sho wn) . As a result , the e volv i ng slo w p hase in the tr ansmembra ne potential ki neti c s lead s to in hibition of e lectro n trans fer in po tenti al -dep enden t reacti ons o f P S II. S uch i nh ibition, in its tum, hinders the rise in the <':6 co nte nt to p roduc e the interm ed iate mi nimum in its dy na mics (Fig. 6b), whi ch ul timatel y re sults in appeara nce o f the sho ulde r (I) on the i nduc tio n c urve (Fi g. 6a) .
/

The breakdown of the abov e-de scr ibed qu a siste ady state o ver 30 0-600 ms (Fi g . 6c) is i n a ll proba bi lity c aused by acti vati on o f t he PS I pro ce sse s, with e n hance me nt o f cyc l ic elec tron tr an sfer re sultin g m
B IO PH YS ICS V"I. " 7 x., () 20()2


KINETIC MODEL OF PRIMARY PHOTOSYNTHETIC PROCESSES

979

competition far PQ between PS II and the blf complex. As a consequence, PS 11 accumulates states with vacant QIJ site (g family), whereas the extent of reduction of the b hemcs increases to retard the plastoquinol reoxidation at the hlf luminal side. This leads to accumulation of PQH 2 in the rhylakoid membrane and ensuing accumulation of the PS IT states with reduced QB (z family). Elevated concentrations of the fluorescing forms g6 and Z6 results in enhanced fluorescence.

characteristics of primary photosynthetic processes. Testing the model in describing these process is the objective of our further work.

ACKNOWLEDGMENT
The work was supported by the Russian Foundation for Basic Research, project no. 00-04-48919.

REFERENCES
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CONCLUSION
Our kinetic model of primary photosynthetic processes has provided a realistic description of the fast induction of chlorophyll fluorescence in a broad range of light intensity. Modeling has demonstrated that the multiphasic pattern of the uphill part of the fluorescence curve is determined by the temporal changes in the concentrationsof different fluorescing forms of PS II. Each level of illumination produces a certain dynamics of accumulation of the fluorescing states, reflected in the characteristic features of the induction curve. Similar results have been obtained by other researchers [13] with a PS 11 model at high light intensities. Examination of separate blocks of our model demonstrates that to describe the fast phase of induction under intense light it is indeed sufficient to consider only PS IT and plastoquinol reoxidation in the PQ pool. However, adequate description of the process under moderate and weak illumination requires consideration of the whole system of generation and utilization of the transmembrane electrochemical proton gradient, including the functioning of the blf complex, PS I, ATP synthase, and passive ion leakage through the thylakoid membrane; furthermore, account should be taken of the inhibition of some electron transfer step by the transmembrane electric potential. Thus we propo.~e a unified model that successfully describes the fast phase of chlorophyll fluorescence induction at any light intensity, as distinguished from the models Ill, ] J] built for particular cases of only intense or only weak illumination. Moreover, our model admits analysis of the composition of the Ouorescent signal under broadly varied light intensity, as well as detailed investigation of lll.jl and t..pH generation on the thylakoid membrane, ion fluxes, and a number of other important
IjIOl'HYSICS V"i..j.7

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BIOPJIYSICS

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