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B/ol'hYio'i",'. Vol. 4<1. No.4. Z003,l'p. 614-623. Trun."wle, 4. 2003, PI'. 656-665. O,ill;nw Rus.'ifJ/1 TeJ:l Copyri/lhlC 200) h,> K"''Ulenko, U."linin. Gruehev, K",ru!e[.,w;. Kuklw.rsldldl. Ti"",joev. Ri:mo'ehe"lu~ G"J,;hev. Ruhin E"RIi
CELL BIOPHYSICS

Cyclic Electron Transport around Photosystem I: An Experimental and Theoretical Study
I. B. Kovalenko-, D. M. Ustinin2, N. E. Grachev-, T. E. Krendeleval, G. P. Kukharskikh-, K. N. Ttmofeev-, G. Yu. Rlzmchenko-, E. A. Grachev2, and A. B. Rubin 1
j

Biological Faculty, Moscow State University, Moscow, J 19899 Russia 2 Physical Faculty, Moscow Stale University, Moscow, //9899 Russia

Received April 28, 2003 Abstract-Electron spin resonance spectroscopy was used to monitor photoinduced changes in the redox state of P700, a photoactive pigment of phctosystem L in isolated Pisum sativum chloroplasts. The kinetics of the ESR signal from P700 (ESR signal I) was recorded at different concentrations of exogenous ferredoxin, ,A kinetic model was developed for ferredoxin-dependent cyclic electron transport around photosystem I. A multiparticle model was built to directly describe electron transfer in multienzyme complexes and restricted diffusion of mobile carriers in individual compartments (stroma, lumen, intramembrane space) of the system. The two models were compared, and a conclusion was made that the spatial organization of the system plays'a-significant role in shaping the kinetics of redox transitions of nOD.
Key words: photosystem I, cyclic electron transport, kinetic model, multiparticlemodel, ferredoxin

INTRODUCTION
In addition to noncyclic electron transport from water to NADPH, there exists cyclic electron transport in higher plant and alga chloroplasts, which is an antimycin A-sensitive process of charge transfer from the acceptor side of photosystem I to the quinone pool. The physiological role of cyclic electron transport is to generate an' additional proton gradient and to protect against oxidative stress on exposure to bright light. Experimental data, including the data of inhibitor analysis, suggest that plastoquinone PQ and the cytochrome by! complex arc involved in cyclic electron transport (Fig. 1; [1-4]). The characteristics of cyclic transport in isolated chloroplasts depend significantly on the concentration of added ferredoxin, indicating that this mobile carrier also takes part in this process. However, the question arises of the mechaAbbr-eviations; Fd, ferredoxin; FNR, ferredoxin:NADf>+ oxidoreductase; FQR. ferredoxin.quinone reductase; EDTA, ethylenediamine tetraaceric acid disodiurn salt; HEPES, @N-(2-hydroxyethyl)piperazine-@N'-2-ethanesulfonic acid; Pc, plastocyanln: Phe, pheophytin; PQ, plastoquinone; PQH l or QH1,
plnsroquinol: PS.
rhoto~y~tem

nisms whereby electrons are passed from ferredoxin, a hydrophilic carrier that resides in the stroma, to plastoquinone, whose molecules are hydrophobic and are localized within the thylakoid membrane (Fig. 1). Several schemes of this process have been proposed [4-7], including those implicating the involvement of ferredoxin-quinone reductase, a still unidentified membrane enzyme (Fig. 1). Some evidence suggests that its role may be played by ferredoxin.Nxlfl" oxidoreductase (FNR), but there are also arguments against this suggestion [I, 2. 5. 8]. In this study, we used electron spin resonance spectroscopy to monitor photoinduced changes in the redox state of P700, a photoactive pigment of photosystem I, over a time interval from 0.1 to 1.0 s. The kinetics of the ESR signal from P700 (ESR signal I) was recorded at different concentrations of added ferredoxin. To describe these data, several kinetic models were constructed based On different schemes of ferredoxin-dependent cyclic electron transport around photosystem I, and the most adequate model was then determined. A multiparticle model was built to directly describe electron transfer in multienzyme

614


MODELING OF CYCLIC ELECTRON TRANSPORT

615

NAD!"

P7Q

®+t'
of the electron uanspurt

"-------------

Lumen

Fig. 1. Organization of cyclic electron transport in chloroplasts. The scheme depicts the thylakoid membrane and the components ch,~n (PS I, FQR, f'l\'R, and cytochrome btl! complexes; und mobile electron carriers Pc, Fd, and QJ.

Question marks indicate where the mechanism of electron transfer is stillunclear.

complexes and restricted diffusion of mobile carriers in individual compartments (stroma, lumen, intramembrane space) of the system. This model was compared with the kinetic model, and a conclusion was made that the spatial organization of the system plays a significant role in shaping the kinetics of redox transitions of P70D.

EXPERIMENTAL
Thylakoids from leaves of 12-day-old pea seedlings (Pisum sutivum, cultivar Sovershenstvo) were isolated in 0.4 M sucrose containing 3 mM MgC12 , 2 mM KCI, I mM EDTA, and 30 mM HEPES (pH 7.8). The isolated thylakoids were stored frozen in liquid nitrogen containing 20% glycerol. Before experiments, the thylakoids were washed in 0.2 M sucrose containing 6 mM MgC12 and 30 mM Tricine (pH 7.6). Ferredoxin was isolated from pea leaves as described by Mutuskin et at. [9]. The photoinduced ESR signal I (g = 2.0025) from P700+ was recorded with a PC-interfaced RE-1307 X-band spectrometer (NTO AN, Russia). The data were stored as averages of every ten replicate measurements. Light from a KGM-300 halogen lamp passed to a cuvette through a set of hear-blocking filters. The reaction mixture was O. J rnj in volume and contained SO mM Tricine (pH 7.5), 5 mM MgCI 2, 6 mM glucose, 2 mM NH 4Cl, 400 U/ml catalase, 40 ~M ferredoxin (unless otherwise indicered). :.1nd rhylakoids (chlorophyll content. 0.1 mg)
BIOPHYSICS Vol. -1:-;
No. -I

To create a pool of reduced ferredoxin required for cyclic electron transport, the thylakoids in the reaction mixture were illuminated with intense white light from a incandescent lamp for 30 s. On the 30th s of illumination, 10 IJ-.M diuron was added to the reaction mixture to block electron transport from photosystem II. To make the reaction mixture anaerobic, it was placed under argon and supplemented with 4 U/mJ glucose oxidase. The agents whose effects were studied were added after diuron. The sample prepared in this w"y was transferred into a spectrometer cuvette and illuminated for l.5 S, after which the kinetics of dark reduction of photooxidized P70o+ was recorded. The kinetic data were analyzed using a nonlinear regression routine of the Mathcad 7 program.

RESULTS

Experimental Data Typical examples of the experimental kinetics of the ESR signal 1 are shown in Fig. 2, Switching on the light causes P700 oxidation, as judged by a sharp rise in the amplitude of this signal to some stationary level. The kinetics of the subsequent dark reduction was fit well with a slim of two exponential functions. The table summarizes the kinetic parameters of the fast and the slow phases of this process obtained by deconvoluting the experimental curves into two exponential components. Their amplitudes, time constants. and the contribution of the fast component to the total stgnal were determined for several roncenuatious (If

](){\.'


6 16
A ( t) . ar b. u n .

K o v A L EN KO " I a i .

Sc he lle r [7 J t ha t the s low phas e o f P 700 red uc tion is acco u nted for b y th e non un iform d o no r en vi ro nm ent a nd on ly brin gs thi s p ro ces s to co mp leti o n . To inter p r e t t h e e xp eri m e nta l da ta fo rm a lly , we b uil t ki n e tic m od el s .

K i ne tic M od e l: Description
and Re sults of Mode lin g The ki n e tic s of t he E SR si gna l 1 is det er mi ned b y th e fo llo w ing p ro ce s se s in t he sy s te m un de r st udy . TInd er acti on of li gh t . p hoto s y s tem I ca ta lyzes o xide l ion o f pl a st oc ya nin ( P c ) on th e lu me na l s id e o f th e t hyl a ko id me mb ra ne a nd red uc ti o n o f fe rr edo xin on i LS s tro ma l si de. Th e y a re foll o wed by ox ida tio n of f e rr e do xin an d r edu c t ion of th e pl as to qu in o ne p ool. G ive n th at ferred ox in m olecul e s are locali zed w ithi n the stro ma an d tha t pl as toq u ino n e i s a h ydroph obic ca rri e r res id ing in the lip id la ye r of the me mb rane , t he s e e vents a rc l ike ly to be medi at ed by me mb rane e xp o s ure of a pro t e in w ith FQR act i vi ty to t he str oma. The subs eq ue nt oxi d at i on (If p l ast oq u in one mv olves f th e cy t oc hro m e htl comp le x a n d r e s ult s in the red uct io n of pl ast oc ya ni n , wh ic h is loc a l ized in th e lume n: ( F i g . 1) . W e b u ilt a set o f incre as ing ly c o mplex k inet ic m ode l s. wi t h m os t de ta i led o f t he m t a k ing acco u nt of t he pro ce s ses of f e rr e do xin doc ki n g on t he accepto r sid e of p hc tosys rem I , th e invo lv e men t o f t he cy toc h ro me tra n sme mb ran e co mple x in red o x rr a nsiuo n s o f pl as toqui no ne , i n te rac tio n o f th e la tte r with th e cy to c hro me c o mple x, a nd t he tw o- elec tro n nature of t his ca rrier . Th e sc he me c " t h e m ost com ple te mo de l i s p re s e nted in Fi g . 3 . Thi s m ode l in co rp or a tes e ve n a hyp ot hetica l FQ R complex .

2
Fi ~. ~.

4

6

8

10

t. s
T emporal e velun o n of the photoin duc ed ESR
1;11,; -

=

nat I fro m catio n radica l P7 CO i n th e dar k for two co nceetr ~ t ions o f e xo g eno us fe rred o x in. S olid l i n e ~ are a bi-e xaone nti ej lit to tile experi ment al c urve s : II U ) '" A ,b(lC - k It) + A zc x p ( - k~t l . w here A l and A , are the ::u n p lnudc s o f the fa sl an d slow c om p one nt s . t e s pectively ; " 1 an d kz a re the i r t ime cons ta nt s ( se e t a hle ): and 11

i s th e c on ce ntr a ti o n rati o of exogenous Fd to PS I .

ad d e d fe r re d o xin . A s c an be s ee n in th e ta ble , th e chara ct e ri sti c t im e wa s about 200 ms for th e f ast co m po ne n r and 2-5 5 for the slo w co mpo ne nt. At hig he r c o nce ntra tio ns o f added fe r red o xi n , the re la t ive co ntri bu t io n of the fa st co m pone nt to P700· red uction was greate r. H o we ve r. t he ch ara c teri st ic t im e of the f a st compo n e n t ( r ec iprocal o f the li me co n stan t ) \-' M ied little w i th th e fe rr e d o xi n co nc e ntra tion. I n cont rust . t he t im e c o n s ta n t o f the s lo w co mponent was lar ge r 0.1 hi g h er fe rr e d o xi n co nce n uu rion:·. III o the r wor d s , fe rr e d ox in acc e ler ated the sl o w ph a se . T hi s ob se r vati on s up p ort s th e sug ge st i on put f or war d by

K i netic panun c iers o f dark reda ction of phorooxidized P700+ in pC rt ifl i 'l (' nt " o n '· (' 11 1 '- · lt i n n ~ o f added ferred o xin

Cc nccnuauo ns of add ed fe rred oxin . A

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T: are l h(' ir c hamc rer is ric um es the la st l" h k- column s ho ws (he {" (\nt rll'lm irm 01 t he rast cornpone m 10 th e to ta l sig n al.

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MODELING OF CYCLIC ELECTRON TRANSPORT

617

Q

----kg

:ko

:A
ut

--_:'-'.,,_

'.

R
.

..... f ..

___ J

: ·out

i

k Q.

_

Pool of nonspecific electron acceptors and donors
Fig. 3. Scheme for the kinetic model of cyclic electron transport around photosystem 1. Boxes stand for PS I, FQR, and cytochrome btl! complexes; P700, pigment of the PS I reaction center; A, generalized acceptor; R, Rieske center; b, high-potential cytochrome b;\; Fd, ferredoxin; Pc, plastocyanin; Q, plastoquinone; Q--, plastoquinol; Qn' semiquinone at the nth site of the cytochrome complex (on the outer side of the membrane). Arrows indicate electron transport pathways; kin' k"Ul' k i , ... , k l ·1, and k l 4 are the rate constant for the respective reactions of electron transfer. Dashed lines depict the boundaries of the mytakoid membrane and the boundary of the pool of nonspecific electron acceptors and donors.

Electron transfer within multienzyme complexes was described by equations for the probabilities of particular states of these complexes. In the model, we used the reduced schemes of the states of the complexes. We did not go intn details of electron transfer within the complexes, because the characteristic times of these stages are much shorter that the characteristic times of the processes that we observed in the experiments (0.1 s). Interaction of the complexes with mobile carriers was described by equations derived from the Jaw of mass action [10, 1 1]. For the photoreaction center complex of photosystem I, the scheme of its states is given in Fig. 4a. This complex is supposed to comprise the primary electron donor P700, the generalized acceptor, and the ferredoxin binding site. The cytochrome bEl! complex (Fig.4b) is regarded as consisting of two catalytic components-the Rieske center and the high-potential cytochrome bh-and the binding site for plastoquinone O; Electron transport through the cytochrome complex is known as the Q cycle. Ferredoxin bound to the complex is thought to be in dynamic equilibrium with free ferredoxin in solution. We assumed
BIOPHYSICS

that a separate protein complex exists that acts as FQR (Fig. 4c) and for which six states are possible. The kinetic model corresponding to the scheme in Fig. 3 is a set of 26 ordinary differential equations. The model variables are the probabilities of particular states of the complexes and the relative concentrations of reduced mobile carriers (plasrocyanin, ferredoxin, and plastoquinone}, The initial conditions were specified according to the stationary electron distribution in the absence of light. The set of model equations was solved numerically using the Model Vision Studium program [12]. The model parameters were chosen from the literature data. The "light" constant k o was assumed 10 be proportional to the light intensity l: kn = lc, where a is the effective section of light absorption by photosystem I. For a light intensity of 500 W/m~ (OUI experimental conditions), ko = 250 S-I [13-J5J. As in the study by Hope et at. [16], the rate constants k 4 , k.', k 6 · and k 7 for the reactions in the cytochrome complex were set to 50, 457, 10 000, and 4000, respectively. For the reaction between plastocyanin and P700, the

vor.

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618

KOVALENKO et at.

(b)

(0)

CD
I I

QJ
r , ,

(j)
I ,

@
I

I;" I:; I :: I ~4_ I:" I '::- I:" I
k~~
k7 Pc

~~,~~

------k-, Pc

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h
R

~

@D;
b
R+

~

k4

Q--

Q)~;
b:
R

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Fig. 4. Scheme of the states of the complexes involved j n cyclic electron transport around photosystcm f: (a) photoreaction [enter (I f PS J, including the pigment P700 (P700) and the generalized acceptor (Al; (h) cytochrome b(/f complex, including the Riecke center (R), high-potential cytochrome b (/}) and plastoquinone at the nth binding site of the complex on the outer surface ofthe membrane (On); and (el FQR complex. Each box stands tor a particular state ora particular complex, which is determined hy the redox slales of individual electron carriers contained in that complex. Arrows indicate the electron transport pathways; k"" k"ul' k], ... , k 1 fwd k l 4 are the rate C0115t:1I1t for the respective reactions of electron transfer. 1,

rate constant (k l ) was set to 4000 [16, 17]. The value of the rate constant k 1 ] (k]J = 50 000) for the reaction between photosystem 1 and ferredoxin was taken from [18J. The other reaction constants were varied. The model kinetics of redox transitions of P700 is shown in Fig. S. These curves are similar to the experimental ones (Fig. 2) in that the fast phase of P70Q+ reduction, which is due to cyclic electron transport, can be approximated well with a single exponenr Moreover, in the model (Fig. 5), as in the

experiment (Fig. 2), the reduction of P700+ by virtue of cyclic electron transport does not proceed to completion, because a small fraction of electrons remain "trapped" after illumination in the stroma in the form of reduced molecules of semiquinone and ferredoxin, or by other groups. It is natural that P700 would be reduced with time from nonspecific donors. Therefore. the entire curve for the reduction of photooxidized P700 can be approximated with a sum of two exponential functions.
BJOJ'HYSICS
VlI!.4/; Nu4


MODELING OF CYCLIC ELECTRON TRANSPORT

619

Analysis of the model results shows that the amplitude arid the contribution of the Iast component to the dark reduction of P70D depend on the concentration of added ferredoxin (Fig. 5). Let the extent of reduction of the latter be fixed. Then, given that diuron blocks the electron influx from photosystem II and the water-splitting complex (which is a natural electron donor), we obtain that the total number of electrons in the system would increase with the ferredoxin concentration. Hence, more electrons would be involved in the system of cyclic transport around photosystem 1. As a result, the amplitude of the fast component of P70D reduction and thereby the relative contribution of this component to the overall effect would grow. However, the fast-phase rate of P70a reduction would not increase, because it depends on the transfer rates of eiectrons at various stages of the cyclic pathway, which remain unchanged. The slow phase of the reduction process can be described in the model by incorporating either a weak flux through the system or a large nonspecific electron pool, From which electrons required for the completion of P70D reduction may be taken. The rate of this slow nonspecific phase is likely to increase with the number of electrons in the system (table).
What is the nature of the slow phase? The

P700+, arb. un.
1.0

»<

TJ""l TJ=:=2
"1]",,4

0.5

~=6

_TJ "" 8 TJ =:= 10

o

2

4

6

8

10
t, s

Fig. 5. Time course of thnk reduction of phctooxidizcd

P700, as calculated in the kinetic model for different valnes of the Fd-lO-PS I concentration ratio 'fl.

photoactive pigment of the photosystem I reaction center is a powerful oxidant [18,19]. Therefore, when the reduced specific donor plastocyanin is absent, electrons can be transferred, albeit slowly, to oxidized P70D from other, nonspecific donors. As suggested by Scheller [7], the slow phase of P700 reduction reflects the ability of P7DO+ to remove electrons from the surrounding molecules, because this reaction can proceed even in the presence of oxygen. Scheller [7] also indicates that the slow phase resembles the reaction observed in the isolated photosystem I complex. The slow phase has also been described in the reduction of P700 oxidized with a flash of light [20J. However, Hope et al. [20] refer to this reaction as nonphysiological. The results obtained with our model support these suggestions. Direct Modeling of Cyclic Electron Transport around Photosystem I The kinetic approach to modeling of primary photosynthetic processes has a number of flaws. The main flaw is the inability to take into account the spatial structural heterogeneity of the system. The use of the law of mass action is justifiable in modeling the
810PlIYSlCS

interaction of isolated fragments with exogenous donors and acceptors in solution. Only in this case can the system be relatively homogeneous. However, in the native thyJakoid membrane, multienzyme complexes interact with mobile carriers in different compartments of the system (with ferredoxin, in the stroma; with plastoquinone, in the lipid bilayer of the membrane; with plastocyanin, in the lumen; Fig. l) At least in two of these compartments, namely, in the intramembrane space and the lumen, free diffusion is impossible because of the size limitations: the protein complexes often span the entire compartment where they are embedded. An a priory assumption that diffusion is free in the stromal space may also be invalid. Although the stromal space is large, the conditions for free diffusion are not satisfied near the membrane because of the presence of the protein complexes and their reaction centers. With a kinetic approach to modeling, it is difficult to describe docking, conformational rearrangements, and other processes, in which the spatial organization of interacting elements may affect their function. All these processes can be simulated by means of "direct," or multiparticle modeling. In this study, we built a multiparticle model of cyclic electron transport around photosystem 1, which includes all the components shown in Fig. 6. The model is organized as a three-dimensional stage (Fig.6) made of the thylakoid membrane, the intruthylakoid space. and the lumen and filled with pigment-protein complexes (photosystem I. the

v,s.

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4

:U03


620

KOVALENKO et ut. Stroma
,~ .G:1 .~

<, /
-

»>

Ferredoxin

Lumen

Photosystem I

Plastocyanin
Fig. (,. Visualization of the three-dimensional stage for the "direct" model of cyclic electron transport around photosystem L Segments at the tbylakoid membrane, lumenal space, and stromal space are shown

cytochrome complex, and FQR) and mobile electron carriers (plastocyanin, ferredoxin, and plastoquinone). To model the motion of plastccyanin. Ferre, doxin, and plastoquinone in their respective compartments, we used the mathematical formalism of the theory of Brownian motion, taking into account the constraints imposed by the organization of the model stage specified above. In our model, we assume that particles move in a viscous medium under the action of random forces arising during collisions with the molecules constituting the medium. As shown in !21J, their motion can be simulated with the Langevin equation, describing how each particular coordinate varies with time under the action of a random force:

increment was chosen so that we had the square root of variance of particle displacement (root-meansquare displacement) approximately equal to onetenth of the mobile carrier diameter. The choice of the time step size in this way ensures a reasonable accuracy and an acceptable computation time. At the right and left boundaries, toroidal (periodic) conditions were imposed. We also took into account the possibility of particle repulsion from physical surfaces, including those of the membrane and protein complexes. Any moving particle could either carry an electron or not. In animation, particles with and without electrons came in different colors. The states of the complexes, the mechanisms of their interaction with the carriers, laws of motion for carriers were specified according to a set of certain rules. At the level of detail used, these rules were as follows (Fig. 6). The inner space of the thylakoid (lumen) is bounded with the membrane. Within the lumen, there are moving particles of plastocyanin. which are capable of carrying an electron. Outside the thylakoid (in the stroma), there are moving particles of ferredoxin, which are also capable of carrying an electron. The membrane contains integral protein complexes (photosystem 1, cytochrome, and FQR) spanning it. Their concentrations and sizes were estimated from the literature data [18, 22, 23]. The photo system T complex can accept an electron from
LlIOJ'HYSICS V"I..)K No

where ~ is the friction coefficient, and.fit) is a random force. The random force has a normal distribution with mean 0 and variance 2kIC" where k is the Boltzmann constant, and T is temperature. The fric, tion coefficient for a spherical particle of radius a reads

where 11 is the medium viscosity. This equation was solved numerically using the adaptive time step scheme Specifically. at any given step. the time

-+

11lm


MODELiNG OF CYCLIC ELECTRON TRANSPORT

621

plastocyanin, transfer it under the action of light across the membrane, and pass to ferredoxin. This mechanism does not operate in the dark. Therefore, the probability of electron transfer from P700 to A was assumed proportional to the light intensity in the model. The next steps of cyclic electron transport are the oxidation of ferredoxin in the stroma and the reduction of plastoquinone in the membrane, in which the FQR complex is involved. Oxidation of plastoquinone and reduction of lumenal plastocyanin proceed by the Qccycle mechanism and involve the transmembrane cytochrome complex [J 8]. In its turn, plastocyanin is a donor for the photoactive pigment P700 (which is the donor part of the photosystem I complex). Thus, the cycle is closed. The mechanism of electron transfer is as follows: if a mobile carrier moving by Brownian diffusion (chaotically) approaches the protein complex by a distance shorter than the effective radius of their interaction, there is a probability of the carrier docking to the complex. The effective radius of interaction is a model parameter that characterizes the maximum distance from which docking is possible. The effective radii of interaction were set equal to the sizes of interacting proteins. This assumption means that docking could take place only upon their collision. The probability of docking is also a model parameter. The effective radii and the probabilities of docking of mobile carriers to the complexes can be assessed by studying their effects in the kinetic constants of interaction of, for example, plastocyanm with photcsystern I. Knowing (from the experimental data) the constant for P700 reduction (interaction of P700 with plastocyanin), we can choose the effective radius and the docking probability in a range allowing the frequency of individual reduction events to agree well with the experimentally determined value of the kinetic constant (the characteristic time) of P700 reduction. After docking, some time elf (also a model parameter) passes during which the complex between photo system I and plastocyanin undergoes conformational changes required for electron transfer from plastocyanin to photosystem I. Thereafter, the oxidized plastocyanin resumes Brownian motion. The direct model and the kinetic model described above are capable of reproducing the kinetic curves of dark reduction of photooxidized P700 obtained experimentally and can be used in kinetic studies of the other mode] variables. 111 addition. direct
BIOPHYSICS V'll.4S i\u.4 21l()]

P700,

arb. un.

50
45 40

3S
30 25

20
15 10

: ~~-=~;E;:::f=*=t;;:~,,-600 1000 1400 200 1800
r.ms
Fig. 7. Kinetics of dark reduction of photooxidized P700,

as calculated in the

multiparticle model

for cases when

PS I, cyt ttl!, and FQR are uniformly distributed in the membrane (dashed line) and when PS I, cyt bflfform a

complex (solid line). Each kinetic curve is an average of ten replicates of the numerical experiment. modeling makes it possible to study how the characteristics of the system depend on the spatial distribution of pigment-protein complexes in the membrane, the geometric parameters (shape and size) of the carriers, the parameters of docking of mobile carriers to molecular complexes, and 011 other characteristics of the system. By way of example, Figure 7 shows two curves of dark reduction of photooxidized P700 calculated in the direct model. The dashed line corresponds to the uniform distribution of the protein complexes (PS 1, cyr brlf, and FQR) over the thylakoid membrane. The solid line corresponds to the case when the photosystem I and the cytochrome brlf complexes lie close to each other and form a supercomplex. In both cases, the kinetic curves are approximated well with a single exponential function. The formation of a supercomplex results in a shorter characteristic time of dark reduction, because there is no need for plastocyanin to diffuse from the cytochrome complex to photosystem I in this case. The possibility of the existence of such a supercomplex is discussed in the study by Bendall and Mauasse [2]. Note that the kinetics of dark reduction of photooxidized P700 calculated for the random spatial distribution of all the three protein complexes coincides with that calculated for the case when only the cytochrome complex is assumed to be distributed randomly, whereas the other two complexes occur in pairs. This result rnav indicate that the


622

KOV ALENKO et al.

limiting stage is electron transfer from plastoquinone to plastocyanin via the cytochrome btl! complex. The modeling thylakoid hensively opportunities afforded by the new type of of primary photosynthetic processes in the membrane will be assessed more comprein future studies.

complexes over the thylakoid membrane. These questions, as well as the role and the effects of electric and electrochemical potentials, which have not been addressed in the direct model proposed, are the subject of future research.

ACKNOWLEDGMENT DISCUSSION
The wcrk was supported by the Russian Foundation for Basic Research (projects nos. 03-04-49 048 and 01-07-90 131).

It is common to use a kinetic approach in modeling the processes of electron transfer in photosyntheSIS. To simulate electron transfer in multienzyrne complexes, equations for the probabilities of particular states of the complexes are employed, along with equations describing interaction of the complexes with mobile carriers that are derived from the law of mass action [10, 11. 24]. We used this approach to simulate electron transfer in isolated fragments of photo system I in the presence of exogenous donors and acceptors. The models developed and the results of identification of the parameters of the system were reported in our previous publications [10, 25, 26]. It was admissible to derive equations describing redox reactions of exogenous mobile carriers with photosynthetic reaction center complexes from the law of mass action occause they freely diffused and interacted in solution. However, the spatial organization of the native thytakoid membrane is such that the assumption of free diffusion does not hold.
In recer.r years, considerable data has accumulated concerning the structure and regulation of photosynthetic processes that has yet to be brought together within a unifying functional framework. The methods of modern object-oriented programming and ever-increasing software and hardware availability make it possible, at least in principle, to integrate the structural and kinetic notions. In this connection, "direct" modeling seems very promising. In this study, we attempted for the first time to describe cyclic electron transport around photosystem 1 by this method Direct modeling allows the researcher to test the validity of the approaches used in kinetic modeling and to assess the range of applicability of the latter. The models developed by this method make it possible (i) to analyze the effects of the structural characteristics of the system on the rate constants and other parameters of kinetic models, and (ii) to clarify the role of the spatial heterogeneity of the system, for example. of rhe nonuniform distribution of multienzyme

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