Cyclic Electron Transport around Photosystem I: An Experimental ...

B/ol'hYio'i",'. Vol. 4

MODELING OF CYCLIC ELECTRON TRANSPORTNAD!"P7Q®+t'"------------- Lumen615Fig. 1. Organization of cyclic electron transport in chloroplasts. The scheme depicts the thylakoid membrane and the componentsof the electron uanspurt 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 carriersin individual compartments (stroma, lumen, intramembranespace) of the system. This model was comparedwith the kinetic model, and a conclusion wasmade that the spatial organization of the system playsa significant role in shaping the kinetics of redox transitionsof P70D.EXPERIMENTALThylakoids from leaves of 12-day-old pea seedlings(Pisum sutivum, cultivar Sovershenstvo) wereisolated in 0.4 M sucrose containing 3 mM MgC1 2 ,2 mM KCI, I mM EDTA, and 30 mM HEPES (pH 7.8).The isolated thylakoids were stored frozen in liquidnitrogen containing 20% glycerol. Before experiments,the thylakoids were washed in 0.2 M sucrosecontaining 6 mM MgC1 2 and 30 mM Tricine (pH 7.6).Ferredoxin was isolated from pea leaves as describedby Mutuskin et at. [9]. The photoinduced ESR signalI (g = 2.0025) from P700+ was recorded with aPC-interfaced RE-1307 X-band spectrometer (NTOAN, Russia). The data were stored as averages of everyten replicate measurements. Light from a KGM-300halogen lamp passed to a cuvette through a set ofhear-blocking filters. The reaction mixture was O. J rnjin volume and contained SO mM Tricine (pH 7.5),5 mM MgCI 2 , 6 mM glucose, 2 mM NH 4Cl, 400 U/mlcatalase, 40 ~M ferredoxin (unless otherwise indicered).:.1nd rhylakoids (chlorophyll content. 0.1 mg)To create a pool of reduced ferredoxin required forcyclic electron transport, the thylakoids in the reactionmixture were illuminated with intense white lightfrom a incandescent lamp for 30 s. On the 30th s of illumination,10 IJ-.M diuron was added to the reactionmixture to block electron transport from photosystemII. To make the reaction mixture anaerobic, it wasplaced under argon and supplemented with 4 U/mJglucose oxidase. The agents whose effects were studiedwere added after diuron. The sample prepared inthis w"y was transferred into a spectrometer cuvetteand illuminated for l.5 S, after which the kinetics ofdark reduction of photooxidized P70o+ was recorded.The kinetic data were analyzed using a nonlinear regressionroutine of the Mathcad 7 program.RESULTS**Experimental** DataTypical examples of the experimental kinetics ofthe ESR signal 1 are shown in Fig. 2, Switching on thelight causes P700 oxidation, as judged by a sharp risein the amplitude of this signal to some stationarylevel. The kinetics of the subsequent dark reductionwas fit well with a slim of two exponential functions.The table summarizes the kinetic parameters of thefast and the slow phases of this process obtained bydeconvoluting the experimental curves into two exponentialcomponents. Their amplitudes, time constants.and the contribution of the fast component to the totalstgnal were determined for several roncenuatious (IfBIOPHYSICS Vol. -1:-; No. -I ](){\.'

6 16 Ko v ALEN KO " I ai.A (t) . arb. un.2 4 6 8 10t. sF i ~ . ~ . Temporal evelunon of the photoinduced ESR 1;11,;nat I from cation radical P7 CO in the dark for two co nceetr~ t ions of exogenous ferredoxin. Solid l i ne~ are abi-exaonentiej lit to tile experimental curves: II U ) '"=A ,b(lC - k It) + Azcxp(- k~t l . where A l and A , are the::unplnudc s of the fasl and slow components. tespectively; " 1and kz are their time constants (see tahle ): and 11is the concentration ratio of exogenous Fd to PS I.added ferredoxin. As can be seen in the table , thecharacteristic time was about 200 ms for the fast componenrand 2-5 5 for the slow co mponent. At higherconcentrations of added fer redoxin, the relative contributionof the fast component to P700· reductionwas greater. However. the characteristic time of thefast component (reciprocal of the lime constant) \-' M ied little with the ferre doxin concentra tion. In contrust.the time constant of the slow component waslarger 0.1 higher ferredoxin concenuu rion:•. III otherwords, fe rredoxin accelerated the slow phase. Thisob servation supports the suggestion put forward byScheller [7 J that the slow phase of P700 red uction isaccounted for by the nonuniform donor envi ronmentand only brin gs this process to completi on. To interpretthe experimental data formally, we built kineticmodels.Kinetic Model: Descriptionand Results of Modelin gThe kinetics of the ESR signal 1 is deter minedby the following processes in the system under study.TInder action of light. photosystem I catalyzes oxidelionof plastocya nin (Pc) on the lumenal side of thethylakoid membrane and reduction of ferredoxin oniLS stro mal side. They are foll owed by oxidation offerr edoxin and reduction of the plastoquinone pool.Given that ferredoxin molecul es are localized withinthe stroma and that plastoquino ne is a hydroph obiccarrier residing in the lipid layer of the membrane,these e vents arc like ly to be mediated by membraneexposure of a protein with FQR activity to the stroma.The subsequent oxidation (If plastoquinone mvolvesthe cytochrome htlf comp lex and results in the red uctionof plastocyanin, which is localized in the lumen:(Fig. 1).We built a set of increas ingly complex kineticmode ls. with most detailed of them taking account ofthe processes of ferredoxin doc king on the acceptorside of phc tosysrem I, the invo lvement of the cytochrometransme mbrane comple x in redox rransiuonsof plastoqui none, interaction of the latter with thecytochrome complex, and the two-electro n nature ofthis ca rrier. The scheme c" the most complete modelis presented in Fig. 3. Thi s model incorporates even ahypothetical FQ R complex.Ki netic panun ciers o f dark redaction of phorooxidized P700+ in pC

MODELING OF CYCLIC ELECTRON TRANSPORT 617-----Q: A:k outkg'.--_:'-'.,,_ .R.....f ..Pool of nonspecific electron acceptors and donorsi k Q.: ·out___J_Fig. 3. Scheme for the kinetic model of cyclic electron transport **around** photosystem 1. Boxes stand for PS I, FQR, andcytochrome 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 nthsite 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 themytakoid membrane and the boundary of the pool of nonspecific electron acceptors and donors.**Electron** transfer within multienzyme complexeswas described by equations for the probabilities ofparticular states of these complexes. In the model, weused the reduced schemes of the states of the complexes.We did not go intn details of electron transferwithin the complexes, because the characteristic timesof these stages are much shorter that the characteristictimes of the processes that we observed in the experiments(0.1 s). Interaction of the complexes with mobilecarriers was described by equations derived fromthe Jaw of mass action [10, 11].For the photoreaction center complex of photosystemI, the scheme of its states is given in Fig. 4a.This complex is supposed to comprise the primaryelectron donor P700, the generalized acceptor, and theferredoxin binding site. The cytochrome bEl! complex(Fig.4b) is regarded as consisting of two catalyticcomponents-the Rieske center and the high-potentialcytochrome bh-and the binding site for plastoquinoneO; **Electron** transport through the cytochromecomplex is known as the Q cycle. Ferredoxin boundto the complex is thought to be in dynamic equilibriumwith free ferredoxin in solution. We assumedthat a separate protein complex exists that acts asFQR (Fig. 4c) and for which six states are possible.The kinetic model corresponding to the schemein Fig. 3 is a set of 26 ordinary differential equations.The model variables are the probabilities of particularstates of the complexes and the relative concentrationsof reduced mobile carriers (plasrocyanin, ferredoxin,and plastoquinone}, The initial conditions werespecified according to the stationary electron distributionin the absence of light. The set of model equationswas solved numerically using the Model VisionStudium program [12].The model parameters were chosen from the literaturedata. The "light" constant ko was assumed 10be proportional to the light intensity l: kn = lc, wherea is the effective section of light absorption byphotosystem I. For a light intensity of 500 W/m~ (OUIexperimental conditions), ko = 250 S-I [13-J5J. As inthe study by Hope et at. [16], the rate constants k 4 , k.',k 6 • and k 7 for the reactions in the cytochrome complexwere set to 50, 457, 10 000, and 4000, respectively.For the reaction between plastocyanin and P700, theBIOPHYSICS vor. 4:-; !\u.4 200:'\

620 KOVALENKO et ut.Stroma,~ .G:1 .~Lumen**Photosystem** IPlastocyaninFig. (,. Visualization of the three-dimensional stage for the "direct" model of cyclic electron transport **around** photosystem LSegments at the tbylakoid membrane, lumenal space, and stromal space are showncytochrome complex, and FQR) and mobile electroncarriers (plastocyanin, ferredoxin, and plastoquinone).To model the motion of plastccyanin. Ferre,doxin, and plastoquinone in their respective compartments,we used the mathematical formalism of thetheory of Brownian motion, taking into account theconstraints imposed by the organization of the modelstage specified above. In our model, we assume thatparticles move in a viscous medium under the actionof random forces arising during collisions with themolecules constituting the medium. As shown in !21J,their motion can be simulated with the Langevinequation, describing how each particular coordinatevaries with time under the action of a random force:where ~ is the friction coefficient, and.fit) is a randomforce. The random force has a normal distributionwith mean 0 and variance 2kIC" where k is theBoltzmann constant, and T is temperature. The fric,tion coefficient for a spherical particle of radius areadswhere 11 is the medium viscosity. This equation wassolved numerically using the adaptive time stepscheme Specifically. at any given step. the timeincrement was chosen so that we had the square rootof variance of particle displacement (root-meansquaredisplacement) approximately equal to onetenthof the mobile carrier diameter. The choice of thetime step size in this way ensures a reasonable accuracyand an acceptable computation time. At the rightand left boundaries, toroidal (periodic) conditionswere imposed. We also took into account the possibilityof particle repulsion from physical surfaces, includingthose of the membrane and protein complexes.**An**y moving particle could either carry anelectron or not. In animation, particles with and withoutelectrons came in different colors.The states of the complexes, the mechanisms oftheir interaction with the carriers, laws of motion forcarriers were specified according to a set of certainrules. At the level of detail used, these rules were asfollows (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 thethylakoid (in the stroma), there are moving particlesof ferredoxin, which are also capable of carrying anelectron. The membrane contains integral proteincomplexes (photosystem 1, cytochrome, and FQR)spanning it. Their concentrations and sizes were estimatedfrom the literature data [18, 22, 23]. Thephotosystem T complex can accept an electron fromLlIOJ'HYSICS V"I..)K No -+ 11lm

MODELiNG OF CYCLIC ELECTRON TRANSPORT 621plastocyanin, transfer it under the action of lightacross the membrane, and pass to ferredoxin. Thismechanism does not operate in the dark. Therefore,the probability of electron transfer from P700 to Awas assumed proportional to the light intensity in themodel. The next steps of cyclic electron transport arethe oxidation of ferredoxin in the stroma and the reductionof plastoquinone in the membrane, in whichthe FQR complex is involved. Oxidation of plastoquinoneand reduction of lumenal plastocyanin proceedby the Qccycle mechanism and involve thetransmembrane cytochrome complex [J 8]. In its turn,plastocyanin is a donor for the photoactive pigmentP700 (which is the donor part of the photosystem Icomplex). 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 distanceshorter 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 parameterthat characterizes the maximum distance fromwhich docking is possible. The effective radii of interactionwere set equal to the sizes of interacting proteins.This assumption means that docking could takeplace only upon their collision. The probability ofdocking is also a model parameter. The effective radiiand the probabilities of docking of mobile carriers tothe complexes can be assessed by studying their effectsin 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), wecan choose the effective radius and the docking probabilityin a range allowing the frequency of individualreduction events to agree well with the experimentallydetermined value of the kinetic constant (the characteristictime) of P700 reduction. After docking, sometime elf (also a model parameter) passes during whichthe complex between photo system I and plastocyaninundergoes conformational changes required for electrontransfer from plastocyanin to photosystem I.Thereafter, the oxidized plastocyanin resumes Brownianmotion.The direct model and the kinetic model describedabove are capable of reproducing the kineticcurves of dark reduction of photooxidized P700 obtainedexperimentally and can be used in kinetic studiesof the other mode] variables. 111 addition. directP700, arb. un.5045403S3025201510: ~~-=~;E;:::f=*=t;;:~,,--200 600 1000 1400 1800r.msFig. 7. Kinetics of dark reduction of photooxidized P700,as calculated in the multiparticle model for cases whenPS I, cyt ttl!, and FQR are uniformly distributed in themembrane (dashed line) and when PS I, cyt bflfform acomplex (solid line). Each kinetic curve is an average often replicates of the numerical experiment.modeling makes it possible to study how the characteristicsof the system depend on the spatial distributionof pigment-protein complexes in the membrane,the geometric parameters (shape and size) of the carriers,the parameters of docking of mobile carriers tomolecular complexes, and 011 other characteristics ofthe system.By way of example, Figure 7 shows two curvesof dark reduction of photooxidized P700 calculated inthe direct model. The dashed line corresponds to theuniform distribution of the protein complexes (PS 1,cyr brlf, and FQR) over the thylakoid membrane. Thesolid line corresponds to the case when the photosystemI and the cytochrome brlf complexes lie closeto each other and form a supercomplex. In both cases,the kinetic curves are approximated well with a singleexponential function. The formation of a supercomplexresults in a shorter characteristic time of darkreduction, because there is no need for plastocyanin todiffuse from the cytochrome complex to photosystemI in this case. The possibility of the existenceof such a supercomplex is discussed in the study byBendall and Mauasse [2]. Note that the kinetics ofdark reduction of photooxidized P700 calculated forthe random spatial distribution of all the three proteincomplexes coincides with that calculated for the casewhen only the cytochrome complex is assumed to bedistributed randomly, whereas the other two complexesoccur in pairs. This result rnav indicate that theBIOPHYSICS V'll.4S i\u.4 21l()]

622 KOV ALENKO et al.limiting stage is electron transfer from plastoquinoneto plastocyanin via the cytochrome btl! complex.The opportunities afforded by the new type ofmodeling of primary photosynthetic processes in thethylakoid membrane will be assessed more comprehensivelyin future studies.DISCUSSIONIt is common to use a kinetic approach in modelingthe processes of electron transfer in photosyntheSIS. To simulate electron transfer in multienzyrnecomplexes, equations for the probabilities of particularstates of the complexes are employed, along withequations describing interaction of the complexeswith mobile carriers that are derived from the law ofmass action [10, 11. 24]. We used this approach tosimulate electron transfer in isolated fragments ofphotosystem I in the presence of exogenous donorsand acceptors. The models developed and the resultsof identification of the parameters of the system werereported in our previous publications [10, 25, 26]. Itwas admissible to derive equations describing redoxreactions of exogenous mobile carriers with photosyntheticreaction center complexes from the law ofmass action occause they freely diffused and interactedin solution. However, the spatial organization ofthe native thytakoid membrane is such that the assumptionof free diffusion does not hold.In recer.r years, considerable data has accumulatedconcerning the structure and regulation ofphotosynthetic processes that has yet to be brought togetherwithin a unifying functional framework. Themethods of modern object-oriented programming andever-increasing software and hardware availabilitymake it possible, at least in principle, to integrate thestructural and kinetic notions. In this connection, "direct"modeling seems very promising. In this study,we attempted for the first time to describe cyclic electrontransport **around** photosystem 1 by this methodDirect modeling allows the researcher to test thevalidity of the approaches used in kinetic modelingand 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 characteristicsof the system on the rate constants and otherparameters of kinetic models, and (ii) to clarify therole of the spatial heterogeneity of the system, for example.of rhe nonuniform distribution of multienzymecomplexes over the thylakoid membrane. These questions,as well as the role and the effects of electric andelectrochemical potentials, which have not been addressedin the direct model proposed, are the subjectof future research.ACKNOWLEDGMENTThe wcrk was supported by the Russian Foundationfor Basic Research (projects nos. 03-04-49 048and 01-07-90 131).REFERENCESJ. Krendeleva, T.E., Kukurskikh, G.P., Timofeev, K.N.,Ivanov, RN., and Rubin, A.B., Dokf. Ross. Akad. Nauk,2001, vol. 379, no. 5, pp. 1-4.2. Bendall, D.S. and Manasse, R.S., Biochim: Biophys.Acta, 1995, vel. 1229, pp. 23-38.3. Moss, D.A. and Bendall, D.S., Biochim, Biophys. Acto.1984, vol. 767, PP. 389-3954. Heimann, S. and Schreiber, U., Plant Cell Phvsiol.,1999, vol. 40, pp. 818-824.5. Cleland, R.E. and Bendall. DS. Phatosvnth, Res.,1992, vol 34, pp. 409--418.6. Hosler, J.P. and Yocum, c.F., Biochim: Biophys. Acta,1985, vel 808, pp. 21-31.7. Scheller, H.V., Plant Phvsiol., 1996, vol. 110,pp.187-194.8. Allen, J.F.. TREl\!DS in Planl Science, 2003, vol. 80tpp_ 15-19.9. Mutuskin A.A., Pshenova, K.V., and Kolesnikova,P.A ..Biokhimiya, 1966, vol 31, pp. 924-927.10. Ri znichenko, G.Yu., !togi Nauki i Tckhniki. Ser.:Biofinka. Moscow: VINITI, 1991, p. 3111. Rubin, A.B., Biofizika (Biophysics), Moscow: KnizhnyiDom Universirct, :2000, vol . 2.12. Ben'kovich, E.S., Kolesov, Yu.B., Scnichenkov, Yu.B.,Praktichcskoe modelirovanie dinamicbeskil.n sistcm(Practice of Modeling of Dynamical Systems), St. Petersburg:BKhV-Peterhurg, 2002J3. Dau, H., Photochem. Phoiooiot.. 1Y94, vol. 60,pp. 1-23.14. Lebcdcva G.V., Belyaeva, N.E., Demin, OV., Rizni·chcnko, G.YlI., and Rubin, A.B., Biofizika, 2002,\'01 47. no fi. pp. I044-10SRBIOPHYSICSxm

MODELING OF CYCLIC ELECfRON TRANSPORT 62315. Schreiber, U. and Neubauer, c.. Z. Natuitorsch, 1987,vol. 42c, pp. 1255-1264.16. Hope, A.D., Liggins, J., and Matthews, D.B., Aust. J.Plant Physiol., 1989, vol. 16, pp. 353-36417. Hope, A.B., Biochim. Biophys. Acta, 20:)0, vol. 1456,pp.5-26.18. Malkin, R. and Niyogi. K., Biochemistry & MolecularBiology of Plants, Buchanan, B., Gruissem, W., andJones, R., Eds., American Society of Plant Physiologists,2000, pp. 568-628.19. Photosynthesis, Govindjee, Ed., New York: AcademicPress, 1982, vol. 1. Translated under the Title Fotosinter,Moscow: Mir, 1984, vol, I.20. Hope, A.B., Huilgol, R.R., Panizza, M" Thompson, M.,and Matthews, D.E., Biochim. Biophys. Acta, 1992,vol. 1100, pp. 15-26.21. DoL M. and Edwards, S.F., The Theory oj Polymer Dynamics,Oxford: Clarendon, 1986. Translated under theTitle Dinamicheskaya teoriya polimerov, Moscow: Mir,1999.22. Albertsson, P.~A., TRENDS in Plant Science, 2001,vol. 6(8), ?p. 349-354.23, Albertsson, P.-A., Recent Res. Devel. Bioener., 2000,vol. 1, pp. 143-171.24. Riznichenko, G.Yu., Lebedeva, G.V., Demin, O.V"Belyaeva, N.E., and Rubin, A.B., 1. Biot. Phys., 1999,vol. 25,pp. 177-192.25. Riznichenko, G.Yu., Vorobjeva, T.N" Khrabrova, E.N..and Rubin, A.D., l'hotosynthetica, 199D, vol. 24(3),pp.37-51.26. vorob'eva, I.1:'\., Krendeleva, I.E., Rizrticaenko, c.v..Shaitan, K.V., and Rubin, A.B., Mol BioI., 1983,vol. 17, pp. 82-91.