Chlorophyll a Fluorescence Induction in Higher Plants: Modelling and Numerical Simulation

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1 . theor. iol. (998) 93, 3 5 Article No. jt9869 Chlorophyll a Fluorescence nduction in Higher lants: Modelling and Numerical Simulation ALEXANDRNA STRET,* GVNDEE, RUN. STRASSER* AND RET. STRASSER* *ioenergetics Laboratory, University of Geneva, CH-5 Lullier-ussy/Geneva, Switzerland Department of iophysics, University of ucharest, R-769 ucharest, Romania (Received on December 997, Accepted on 7 February 998) Chlorophyll a fluorescence induction is extensively used as a probe of photosynthesis, and thus, it has become necessary to quantitatively analyse it to extend its usefulness. We simulate the experimental data of fluorescence transients in strong light through numerical integration, both in dark- and light-adapted plants. n the mathematical model used here we have considered for the first time the redox reactions at both the acceptor and the donor sides of photosystem, and the non-photochemical quenching by the oxidised plastoquinone molecules from the lipid matrix of the thylakoid membrane. The model is based on assumptions established in the literature and also the values of input parameters used in simulations. The simulated fluorescence induction curves show the characteristic steps as in the experimental ones and, in specific conditions, the presence of a dip (D) between the and steps of the transient. Moreover, it has been shown here how typical patterns of fluorescence kinetics are influenced by the state of the sample by studying the basic effects of the influence of some parameters [i.e. the connectivity between different S units, initial Q :Q ratio and the ratio of the starting states of the oxygen evolving complex (S :S ), number of plastoquinone molecules in the plastoquinone pool, initial redox state of the plastoquinone pool, and the rate of plastoquinol oxidation]. n this way the information can be drawn from the experimental curves relative to these parameters. 998 Academic ress ntroduction Chlorophyll a (Chl a) fluorescence induction observed in plants, algae and cyanobacteria, known also as the fluorescence transient or Kautsky effect (Kautsky & Hirsch, 93), has been extensively studied (see reviews, Govindjee & apageorgiou, 97; apageorgiou, 975; Fork & Mohanty, 986; Krause & Weis, 99; Dau, 99; oshi & Mohanty, 995; Govindjee, 995). t consists of light intensity dependent polyphasic changes in Chl a fluorescence emission when a dark-adapted leaf, or a suspension of isolated chloroplasts or intact photosynthetic cells, is illuminated with continuous light (see Fig., curves and ). n the first phase of the transient n sabbatical from Department of lant iology, University of llinois, 65 Morril Hall, Urbana, L 68, U.S.A. (time-scale from zero to one or several seconds, depending on the light intensity) the fluorescence intensity rises quickly from an initial low value, F (the level), to a higher one, F (the level). Under low light, fluorescence rises to an intermediary step denoted as F pl (curve, Fig. ), but under high light, typically over 5 W m, two intermediary steps designated as F (the or the level) and F (the or the level) normally appear (curve, Fig. ; see Strasser & Govindjee, 99, 99; Neubauer & Schreiber, 987). The F level becomes saturated from Wm and is then denoted as F M. A dip between and is sometimes present in fluorescence transients and is labelled as D (Munday & Govindjee, 969). t is well established now that the variable fluorescence F V (t) [defined as F(t) F, where F(t) is the fluorescence intensity at any time t] is related 593/98/33 + $3./ 998 Academic ress

2 3 A. STRET ET AL. F(t)/F F 3 F 5 3 F F F pl FG.. Fast Chl a fluorescence induction curves (fluorescence as a function of time from 5 s to s) measured on dark adapted isum sativum leaves illuminated with Wm (curve ), 6 Wm (curve ), and 6 Wm in the presence of DCMU (curve 3). Wavelength of illumination, 65 nm. For definition of symbols, see Glossary. mainly to the fluorescence of the antenna chlorophyll of photosystem (S ), and is due to the variation of the quantum yield of fluorescence emission (between and %) (Latimer et al., 956). The interpretation of the fluorescence signals must always take into account that the quantum yield of Chl a fluorescence is proportional to the rate constant of fluorescence divided by the rate constants of all the various pathways of deexcitation (i.e. fluorescence, heat dissipation, excitation energy transfer, quenching, and photochemistry). As the fluorescence induction measurements are now frequently used in different in vivo studies of plants, such as stress, pollution and productivity (see e.g. Schreiber & ilger, 993), it is very important to know how to correlate the experimental results with the rates of specific biochemical reactions. Therefore, a mathematical model that can be used to simulate and fit the measured data is considered to be very useful. However, most earlier simulations have been made for the simpler case of chloroplasts inhibited with diuron (DCMU) (Hsu et al., 989; Trissl et al., 993; Trissl & Lavergne, 99; and Lavergne & Trissl, 995), where the fluorescence transient has only an (or shape) (curve 3, Fig. ), or for chloroplasts illuminated with low light intensities (curve, Fig. ) (Renger & Schulze, 985; aake & Strasser, 99; aake & Schlöder, 99; Hsu, 99, 993). n this paper, we present a model that simulates experimental (D) fluorescence curves obtained upon exposure of dark-adapted photosynthetic apparatus with continuous strong light illumination (curve, Fig. ). reliminary observations have been F presented (see Stirbet & Strasser, 995, Stirbet et al., 995, and Stirbet & Strasser, 996). The model is based on six main assumptions: () Chl a fluorescence reflects the concentration of the reduced electron acceptor Q A (Duysens & Sweers, 963); () for all practical purposes, the S units are considered homogeneous; (3) excitation energy can be exchanged between several S units (oliot & oliot, 96); () the rate constant of the Q A reduction is modulated by the redox state of the oxygen evolving complex (EC), the so-called S-states (Delosme, 97 ; oliot et al., 97); (5) oxidised plastoquinone pool molecules quench Chl a fluorescence (Vernotte et al., 979); and (6) a so-called two-electron-gate process acts on the acceptor side of S (Velthuys & Amesz, 97; ouges-ocquet, 973). n order to prove the generality of the model, we have also simulated specific fluorescence curves such as those obtained with DCMU treatment or with pre-illumination (light-adaptation) of the leaf. Modelling of the Fast hase of Chl a Fluorescence nduction: Theory and Assumptions Chl a fluorescence emission in vivo comes from both S and S photosystems, the contribution of S being smaller ( 5% of F see Lavergne & Trissl, 995). As S does not contribute to the variable fluorescence (utler, 978), it was not considered here. However, the use of uncorrected fluorescence transients (neglecting S contribution) causes the values of the ratio N = F V /F and of the connectivity parameter C (see below) to be slightly underevaluated. n this paper we only simulate the variable fluorescence induction curves and do not fit them exactly with the experimental data; so neglecting the contribution of S fluorescence does not affect the results. The first phase of Chl a fluorescence induction is mainly related to the photochemical processes and charge separation reactions that take place at the S level (Dau, 99; Govindjee, 995; oshi & Mohanty, 995). Therefore, for the modelling of the fluorescence transients to be precise, the structure and function of these reaction centres must be defined. The S unit catalyses the light-induced electron transport from water to the plastoquinone (Q) pool molecules (mobile electron carriers between S and S ). Figure shows a schematic view of the main electron transport mediated by S, in which, besides water and Q pool molecules, six other components are involved: () the water-oxidising manganese cluster (denoted also as xygen Evolving Complex, EC); () the redox-active tyrosine, Y Z ;

3 CHL A FLURESCENCE NDUCTN SMULATN 33 Light absorption e H e Y Z e S S S S + H + Exciton Exciton * + he he he e S 3 e EC Chl a Chl a e e e Q A Q A Q A Q A Q A Q A Q Q Q H + Q H Q QH Fluorescence S e Cyt b/f e FG.. A schematic diagram of electron transport reactions considered in the model (see text for explanation). Chl a = chlorophyll a antenna; EC = oxygen evolving complex in S n states; Y Z = primary electron donor to 68 + ; = 68, the S reaction centre Chl a; he = pheophytin a; Q A, Q = bound plastoquinones; Q = plastoquinone pool; Cyt b/f = cytochrome b 6/f complex; S = photosystem. (3) the photochemical reaction centre (68) which is the primary electron donor of S ; () one pheophytin a molecule (he) which is the primary electron acceptor of S ; (5) one tightly bound plastoquinone (Q A ); and (6) one loosely bound plastoquinone (Q ). Kinetic measurements support this theory of the structure of the main electron transport chain (see reviews by Hansson & Wydrzynski, 99; Seibert, 993; Diner & abcock, 996, 977). There are evidences for some side pathways of electron transport, but these are ignored in the present model. The electron transport at S level starts with the exciton trapping by the photochemical reaction centre chlorophyll a (68) which induces the primary charge separation: 68 + he (Greenfield & Wasielewski, 996). This primary radical pair can decay by several pathways: transfer of the electron from he to Q A (the secondary charge separation), recombination and reformation of singlet excited state of the photochemical reaction centre 68*, formation of 68 triplet state, and other nonradiative pathways. Under normal conditions, electron flow from he to Q A is the major reaction. Q A, which is a one-electron acceptor, stabilises the charge separation. Subsequently, the reduction of 68 + to 68 occurs by the transfer of one electron from Y Z.Q A reduces a plastoquinone molecule, Q, loosely bound to a specific site on S centre, named the Q -binding site (Crofts & Wraight, 983). The full

4 3 A. STRET ET AL. reduction of Q requires the addition of two electrons; therefore, two photochemical turnovers of the reaction centre are needed (two-electron gating mechanism). Velthuys (98) has suggested that Q remains bound at the Q -binding site before the second reduction, as the affinity of Q binding site is low for Q and QH, but high for Q. nly after the protonation of Q does the plastoquinol (Q H = QH ) unbind from the reaction centre and diffuse into the membrane. Then, an oxidised plastoquinone molecule will (eventually) bind to the Q -binding site, and the process of Q reduction can be repeated. n the donor side of S unit, the oxidised Y Z is reduced by EC. The rate constant for this process depends on the redox state of the water-oxidising manganese cluster (abcock et al., 976). t has been proposed that this dependence is due to electrostatic effects. The EC cycles through the so-called S n states (see Fig. ), the subscript indicating the number of oxidising equivalents in the system. The stepwise accumulation of four positive charges on the oxidising side of S constitutes a condition for the splitting of two water molecules and the release of four electrons, four protons and of molecular oxygen (Kok et al., 97). The oxygen molecule is released during the S to S transition (for reviews, see Renger, 993; ritt, 996). The electron transport chain described above, dealing with the redox reactions around the S centre, is schematically illustrated in Fig.. We have used this reaction scheme in the kinetic analysis of the photosynthetic system. Similar to the models of Renger & Schulze (985) and Hsu (99), the exciton trapping (68 68*) and the primary charge separation (68*he 68 + he ) have been introduced indirectly in the model through the rate constant of Q A reduction, kl. This one is a global rate constant and depends on several parameters, for example light intensity, absorption cross section of the antenna of S units, rate constants of exciton trapping and primary charge separation. The reverse reaction represents the complex process of charge recombination. n the photosynthetic membranes, the S centres do not function in an isolated state. An efficient excitation energy transfer between several S units takes place, that increases the efficiency of the light conversion process. This process is commonly denoted as S connectivity (oliot & oliot, 96; oliot et al., 973) or grouping (Strasser, 978 and 98). t is well known that during the exposure to light of a dark adapted green plant, the primary quinone acceptor Q A accumulates in its reduced form Q A (see for example the review on Chl a fluorescence induction phenomenon by Govindjee, 995). The net Q A accumulates as the plastoquinone molecules of the Q pool become reduced. The plastoquinol (QH )is reoxidised by the cytochrome b 6 /f complex (Cyt b/f), this being the limiting reaction of the linear electron transport chain (Stiehl & Witt, 969; Haehnel, 98). Since the oxidised Q A is a strong quencher of the S fluorescence (Duysens & Sweers, 963), the accumulation of the reduced Q A seems to be the main factor that must be considered when the fluorescence induction is analysed. The photochemical reaction centre of S in its oxidised state, 68 +, is also an efficient fluorescence quencher (utler, 97; Sonneveld et al., 979; Deprez et al., 983; Shinkarev & Govindjee, 993). However, we will not consider 68 + quenching here, because under most conditions, there is no significant accumulation of 68 + as the abundant water molecules keep it reduced via EC and the primary donor Y Z (Dau, 99). ASSUMTNS F THE MDEL n view of the above, since the concentrations of Q A and 68 + depend mainly on the processes occurring at the S level, the first assumption of our model of the fast phase of Chl a fluorescence induction is that the variable fluorescence is related mainly to S kinetics. More specifically, Chl a fluorescence yield mainly reflects the number of the closed S centres during the time interval of our analysis. However, S activity is also indirectly considered, as the rate constant of plastoquinol reoxidation by the Cyt b/f complex depends on the rate of reduction of the S photochemical reaction centre in its oxidised state (7 + ). t must be noted that, for simplicity, in the present model we have considered the reoxidation reaction of plastoquinol to have a first order kinetics. The second assumption of the model is that, on average, all S units have the same kinetic characteristics (a homogeneous S population), and each one of them is served by the same number of Q pool molecules. The third assumption of the model is that the fraction of closed reaction centres, (t)=[q A ] total (t)/ ([Q A ] total (t)+[q A ] total (t)), influences the relative variable fluorescence, V(t)=[F(t) F ]/(F M F ), and the global reduction rate of Q A, kl. Furthermore, according to the theory of the S connectivity (oliot & oliot, 96; Strasser, 978; utler, 98; Strasser, 98; Trissl & Lavergne, 99; and Lavergne & Trissl, 995) the following relationships are valid: (t) V(t)= +C[ (t)] ; ()

5 CHL A FLURESCENCE NDUCTN SMULATN 35 kl = kl +C +C[ (t)] ; () where C will be referred as the connectivity parameter (its value depending on the overall probability of connectivity between the S units see oliot & oliot, 96; Strasser, 978; and utler, 98) and kl is the initial rate constant of Q A reduction. t can be seen that if the photosystems are not connected (i.e. C = ) the relative variable fluorescence is identical to the fraction of closed reaction centres, V(t)=(t), and the rate constant of Q A reduction is constant, kl = kl. The fourth assumption of our model is that the net rate of Q A reduction (kl) depends also on the S n state of EC, it being higher in S and S than in S and S 3 states. This assumption is based on the observation of Delosme (97) and oliot et al. (97), that open S units in the S and S states are better quenchers of fluorescence than in the S and S 3 states. There are two possibilities: increased rate of photochemistry and/or of heat dissipation. We favour the first; therefore, this different quenching capacity is assumed to be due to a higher primary rate constant for photochemistry (kl) for S units in the S and S state. The following relationship between the initial rate constants of Q A reduction, kl, have been used in the simulations: kl = kl =kl =kl 3 (3) where the subscripts refer to the redox state of EC in S unit (i.e. S,S,S,andS 3, respectively). The fifth assumption of the model is that Chl a fluorescence in leaves is quenched also by the oxidised molecules of the Q pool (Vernotte et al., 979). These authors have shown that the quenching is of Stern Volmer type, similar to that obtained with exogenous quinones (e.g. dimethylbenzoquinone and dichlorobenzoquinone see Lavergne & Leci, 993; and Srivastava et al., 995a). t is interesting to note that for both endogenous and exogenous quinones, the Stern-Volmer constant was found approximately four times higher for F M than for F (Vernotte et al., 979; Srivastava et al., 995a). Therefore, the values of the relative variable fluorescence, V(t), have been calculated from the unquenched ones, V u (t), by using the Stern Volmer relationship. ecause several restrictive assumptions have been used in the estimation of the impact of the Q non-photochemical quenching effect on the relative variable fluorescence, the obtained semiempirical relationship (A.7) is only an approximation (see Appendix). The experimental data used in this formula were f cl and f op (the fractions of fluorescence intensity reduced by Q non-photochemical quenching for a system with all S units closed and open, respectively) and the ratio N = F V / F =(F M F )/F. We have used the values f cl =.3, f op =. (Vernotte et al., 979), and N = (Srivastava et al., 995b). Materials and Methods EXERMENTAL MEASUREMENTS n this paper, we have compared our theoretical curves with the data of Strasser et al. (995) on fluorescence transients of dark-adapted and lightadapted leaves. Since these measurements are important to this paper, we have repeated them, and describe below the experimental conditions of these measurements that confirm the earlier observations of Strasser et al. (995). lant material Experiments were done with fully mature intact leaves of 3 week old pea (isum sativum). lants were grown in the greenhouse in small pots with a soil mixture ptima (ptima-werke H. Gilgen, Munchenstein, Switzerland), at C/8 C (day/ night) temperature cycle under natural sunlight, with alternate day watering. Chl a fluorescence induction measurements Chl a fluorescence transients from pea leaves were measured at room temperature, using a shutter-less system (lant Efficiency Analyser built by Hansatech Ltd., King s Lynn, Norfolk, U.K.). Light was provided by an array of six light-emitting diodes (peak at 65 nm) focused on the sample surface to provide homogeneous illumination over the exposed area of the sample ( mm diameter). The light intensity was 6 Wm, for high light conditions, and Wm, for low light conditions. The fluorescence signals were detected using a Nphotodiode after passing through a long-pass filter (5% transmission at 7 nm). The first reliable point of the transient is measured 5 s after the onset of illumination. This point was taken as F as extrapolation of fluorescence to time zero was within 5% of this value. Fluorescence measurements were taken in dark adapted conditions (leaves maintained min in darkness), or in light adapted conditions (leaves illuminated continuously for hr with 8 Wm light intensity and then dark adapted for 3 s).

6 36 A. STRET ET AL. NUMERCAL SMULATN RCEDURE The concentration of reactants in a.5 s time range have been obtained through numerical integration of rdinary Differential Equations systems (DEs) associated with the reactions presented in Fig. 3(a) and (b). n these figures the reaction chains related to S units which are initially in S Q A Q and S Q A Q states [Fig. 3(a)], and in S Q A Q and S Q A Q states [Fig. 3(b)] are shown. For simplicity, we have normalised the total number of S centres in different redox states and the total number of plastoquinones in the pool. For example, at time zero: [S Q A Q ]+[S Q A Q ]+[S Q A Q ]+[S Q A Q ]= and [Q] + [QH ]=n where n is the total number of the plastoquinone molecules in the pool. The S units with Y Z and 68 in the oxidised states (Y + Z and/or 68 + ) have been noted with an asterisk after S n (e.g. S 3 *Q A Q ). Those S n S n + transitions that are much faster than the following (succeeding) reaction in the chain (e.g. S S transition compared to Q A Q Q A Q reaction see Table for the corresponding rate constants) have been considered to take place simultaneously with the light reaction, in order to reduce the number of equations in the DE systems. All the reactions in the considered model are of first order (except Q H -Q exchange reaction, which is of second order) and with a kinetics of mass action type. The loosely bound plastoquinol molecule (Q H ) is replaced by a new Q molecule from the pool, and it diffuses to the oxidation site on the Cyt b/f complex. We have considered that the Q -site is always occupied (with Q,Q,Q,orQ H ). Also, at the beginning of illumination we have assumed that all of the S units are in the open state (i.e. the fraction of closed reaction centres equal to zero, = ) for both types of samples, the dark adapted and the light adapted leaves. The numerical algorithm used for the simulations was the Livermore Solver of rdinary Differential Equations (LSDE) procedure (Hindmarsch, 98), with the initial concentrations of the reactants and the rate constants of the reactions as parameters. We have used the values of the rate constants presented in Table (unless otherwise noted). These values are comparable to those reported in the literature (see references in Table ). efore simulating the experimental curves, it was necessary to evaluate the rate constant for Q A reduction of the reaction centres in state S (kl) in our specific experimental conditions (6 Wm illumination intensity, pea leaves). t was obtained by comparing the simulated transients for different values of kl, and the experimental one of DCMU treated leaves. Theoretical curves have been TALE The values of input parameters used in simulations and the corresponding values from literature nput parameters Dark adapted leaf Light adapted leaf Reported values References N = F V/F Srivastava et al. (995b) f cl ; f op 3%; % 3%; % 3 %; 5 % Vernotte et al. (979) Total number of Q in the pool; (initial ratio Q:QH ) 6; (6:) 6; (:) 5 Lavergne et al. (99) nitial ratio: S :S.8:..8:..75:5 Kok et al. (97) Forbush et al. (97) nitial ratio: Q :Q.7:.3.7:.3.7:.3 Wollman ( 978).5:.5 Rutherford et al. (98) t /; andk eq for: 3 ; 3 s; s; 5 Diner, 977 Q A Q Q AQ Robinson & Crofts (983) t /; andk eq for: 6 s; 6 s; 3 5 s; 5 or Diner (977) Q A Q Q AQ Crofts & Wraight (983) t /; andk eq for: ms; ms; ms; or Crofts et al. (98) Q AQ H +Q Q AQ + QH t / for: QH Q ms 3.5 ms ms Haehnel (976) t / for: S S 3 s 3 s 3 s abcock (987) t / for: S S s s s abcock (987) t / for: S S 3 35 s 35 s 35 s abcock (987) t / for: S 3 S S.3 ms ms.3 ms abcock (987) f cl and f op are the fractions of the Chl a fluorescence that have been quenched by the oxidised Q molecules from the pool, for a system with all S units closed and open respectively; t / is the half time of a forward first order reaction; t / is the half time of a second order reaction (i.e. the Q exchange reaction), with t / = ln /( k E[Q] ); and K eq is the equilibrium constant of reaction.

7 CHL A FLURESCENCE NDUCTN SMULATN 37 (a) S Q A Q kl S Q A Q k A k A kl S Q A Q S 3 Q A Q k A k A kl 3 S 3 Q A Q S 3 *Q A Q k H k H kl 3 k H k H S 3 Q A Q H Q S 3 *Q A Q H Q k E k E k E k E QH kl QH 3 S 3 Q A Q S 3 *Q A Q S Q A Q k A k A k A k A ks kl S 3 *Q A Q 3 S Q A Q S Q A Q k k A A S Q A Q kl S Q A Q k H k H k H k H kl S Q A Q H Q S Q A Q H Q k E k E k E k E QH QH S Q A Q S Q A Q QH k ox QH Q k k A A S Q A Q (b) S Q A Q kl k A S Q A Q k A kl S Q A Q S Q A Q k A k A kl S Q A Q S 3 Q A Q k H k H S Q A Q H Q kl S 3 Q A Q H Q QH QH kl S Q A Q S *Q A Q S 3 Q A Q k A k H k H k E k E k E k E k A k A k A ks kl S *Q A Q S 3 Q A Q 3 S 3 *Q A Q k A k A S 3 *Q A Q k H k H ks 3 S 3 *Q A Q H kl S Q A Q H Q Q k E k E k E QH QH S Q A Q S Q A Q H Q k E k E S Q A Q QH QH k ox QH Q FG. 3. S redox reaction chain for the units initially in (a) S Q AQ and S Q AQ states; (b) S Q AQ and S Q AQ states.

8 38 A. STRET ET AL. obtained considering the values of the rate constants for Q and Q reduction equal to zero. Similar to the experimental DCMU transient (curve 3, Fig. ), they have a characteristic shape (or shape, as we may define it) reaching the maximum values (V =) in several ms (results not shown). The best fit with experimental data was obtained with kl = s, and was used in all the simulations presented in this paper (unless otherwise noted). Finally, the time courses of the various redox states of S units (Q A Q, Q A Q, Q A Q, Q A Q H, Q A Q, Q A Q, Q A Q, and Q A Q H ) have been calculated. We have also calculated using eqns () and (A.7) (see earlier in the theory and assumptions of the model, and the Appendix, respectively), the time courses of the fraction of reaction centres in which Q A is reduced (the so-called closed reaction centres), (t), and the relative variable fluorescence with and without Q quenching, V(t) andv u (t), respectively. n order to compare the shapes of the theoretical curves, the ratios (t)/ max, V(t)/V max,and V u (t)/vmax u have been presented (where max, V max and Vmax u are the highest values of (t), V(t) andv u (t), respectively). Results and Discussions GENERAL REMARKS The curves obtained from simulations of the transients of dark adapted leaves are presented in Fig. (a) and (b). Time courses of the concentrations of closed S units (i.e. [Q A ] total, Q A Q, Q A Q, Q A Q,andQ A Q H, curves 5 respectively), and the ratio [Q](t)/[Q] total (curve 6), are shown in Fig. (a). We note that curve also represents the fraction of the closed reaction centres, as the total concentration of the S units used in simulation was set to be equal to unity. Similar curves of open reaction centres are shown in the inset: [Q A ] total,q A Q,Q A Q,Q A Q, and Q A Q H, curves 7, respectively. t can be seen that at the step two of the redox states of the closed centres, Q A Q and Q A Q, predominate. Although a mixture of different closed forms of S centres is present at and steps, the Q A Q H redox state clearly predominates (see curve 5). The fraction of the closed reaction centres (curve, [Q A ] total = ) has a maximal value close to.8 in this simulation. The value of max depends on several factors such as the initial Q A reduction rate constant, and the rate constant of plastoquinol oxidation (results not shown). t can reach the highest value, max =, when the reaction of plastoquinol oxidation is inhibited (Stirbet & Strasser, 995), which means that the connection between the two photosystems is interrupted. The Q pool is mostly reduced in the interval. The degree of Q pool reduction at steady-state strongly depends on the rate of plastoquinol oxidation (S activity). f this rate is zero (blocked S ), then the Q pool is completely reduced at the level. n Fig. (b) the normalised curves of the fraction of the closed reaction centres, (t)/ max, of the unquenched relative variable fluorescence, V u (t)/v u max, and of the relative variable fluorescence, V(t)/V max, are shown. The absolute curves (t), V u (t) and V(t) are also shown in the inset. The value of the connectivity parameter used in these simulations was C =. The normalised fraction of the closed S centres, curve (t)/ max [Fig. (b)], has higher values than that of the relative variable fluorescence, V(t)/V max, at both the and levels. The figure also shows that the Q quenching phenomenon lowers mainly the level of the normalised relative variable fluorescence curves. To understand how different initial parameters of the model could affect the shape of calculated curves, results obtained with different values for several parameters are discussed below. NTAL RATS F S :S AND Q :Q The initial concentrations of the reactants are important parameters of the model. We have considered here that initially all S units are open (i.e. with Q A in oxidised state), EC is either in the S or S state, and Q is partially reduced in a fraction of centres (i.e. in Q state). This is proposed to be the case for dark adapted samples. Therefore, in our model we have four initial concentrations which are different from zero [S Q A Q and S Q A Q from Fig. 3(a); S Q A Q and S Q A Q from Fig. 3(b)]. These values must be chosen to fulfil some specific S :S and Q :Q ratios, as reported in the literature for the dark adapted situation (see Table Kok et al., 97; Forbush et al., 97; Wollman, 978; Rutherford et al., 98). Figure 5(a f) shows the results of simulation for two values of the S :S ratio (.:. and.8:.) and three values of the Q :Q ratio (.:.,.7:.3, and.5:.5). t can be seen that these different ratios affect both the and steps. The step has higher intensities as the fraction of Q is increased. The step has almost the same intensity, but it can be followed by a dip, more or less deep, depending mostly on the Q :Q ratio. The largest dip is observed for the Q :Q ratio of.5:.5 [Fig. 5(c and f)], a small one for.:. [Fig. 5(a and d)], and no dip for.7:.3 [Fig. 5(b and e)]. From the two S :S

9 CHL A FLURESCENCE NDUCTN SMULATN (a) (t)/ max ; V u (t)/v u max ; V(t)/V max Concentration (rel. units) V u V 5 3 ; V u ; V Concentration 3 D D 5 6 (b) / max V u /V u max V/V max FG.. Typical theoretical curves obtained with our model with input parameters for dark adapted conditions presented in Table. (a) Time course of the concentrations of [Q A ] total =, Q A Q,Q A Q,Q A Q,Q A Q H and Q/[Q] total (curves 6, respectively); [inset in panel (a)] time course of the concentrations of [Q A] total, Q AQ,Q AQ,Q AQ, and Q AQ H (curves 7, respectively); (b) time course of (t)/ max, V u (t)/vmax, u andv(t)/v max where (t) is the fraction of closed S centres at time t, and max, is the highest value of (t); V u (t) is the unquenched relative variable fluorescence at time t, andvmax, u is the highest value of V u (t); and V(t) is the Q-quenched relative variable fluorescence at time t, and V max is the highest value of V(t); [inset in panel (b)] time course of (t), V u (t) andv(t). For explanation of the symbols,,, D, and see the text. ratios used in the simulations, the ratio of.8:. only produced a slight dip. For the ratio Q :Q =.5:.5 we have also observed a decrease of approximately 5 % in the value of the relative variable fluorescence at the level (results not shown). n the present paper we have used the initial ratios S :S =.8:. and Q :Q =.7:.3 in all the other simulations. We must note that we have chosen the value of.7:.3 for the Q :Q ratio, as reported for isolated chloroplasts (Wollman, 978), and not.5:.5, as reported for spinach leaves (Rutherford et al., 98), because normally, the transients in high light of most dark adapted leaves do not show a significant dip.

10 A. STRET ET AL. V(t)/V max V(t)/V max S :S =.:. Q :Q =.:. S :S =.8:. Q :Q =.:. S :S =.:. S :S =.:. Q :Q =.7:.3 Q :Q =.5:.5 D D D (a) (b) (c) S :S =.8:. S :S =.8:. Q :Q =.7:.3 Q :Q =.5:.5 D D D.. (d) (e) (f) FG. 5. Simulated Chl a fluorescence induction curves (V(t)/V max) in dark adapted conditions for different values of initial S :S and Q :Q ratios: (a).:. and.:.; (b).:. and.7:.3; (c).:. and.5:.5; (d).8:. and.:.; (e).8:. and.7:.3; and (f).8:. and.5:.5. For definition of symbols, see the Glossary. S CNNECTVTY An important parameter of the present model is the connectivity parameter, C, which depends on the probability of connectivity between the S units (see Strasser et al., 99). C is the constant for the curvature of the hyperbola, V vs., derived by oliot & oliot (96) and Strasser (978) [see eqn ()]. Figure 6 shows the influence of connectivity on the fluorescence transients of a DCMU treated leaf. We have simulated the fluorescence induction curves for two extreme values of the connectivity Relative variable fluorescence, V(t) C = C = C = 3 Time (ms) FG. 6. Simulated Chl a fluorescence induction curves in dark adapted conditions (see Table ) in the presence of DCMU. Relative variable fluorescence curves, V(t), have been calculated at a fixed initial Q A reduction rate constant, kl = s, but with varying connectivity parameter, C =,, and. parameter (i.e. C = and C = ), and for C =. n the linear time plot, the sigmoidal shape of the simulated curves for C = and can be observed. t must be noted that the sigmoidicity of experimental DCMU transients was the first argument that favoured the S connectivity concept (oliot & oliot, 96). The effect of the connectivity on the fluorescence transient curves simulated for the untreated dark adapted leaf is presented in Fig. 7(a) and (b). The fraction of closed centres, [Fig. 7(a)], and the quenched relative variable fluorescence, V [Fig. 7(b)], both normalised at their highest values, have been calculated for various values of the connectivity parameter (i.e. C =,,.5, and ). The absolute curves are presented in the inserts. According to eqn () from the theory and assumptions of the model, the Q A reduction rate (kl) increases with the number of the closed centres, (t). This increase is more pronounced for larger values of C (e.g. for C =, the kl value when all centres are closed is doubled compared to that when all centres are open, but for C = it is tripled). As a consequence, as the C value increases, an increased number of S centres are closed [see Fig. 7(a) inset] due to a higher electron transport rate. However, the relative variable fluorescence decreases with C [see Fig. 7(b) inset], as the connectivity diminishes the loss of trapped energy as fluorescence, favouring a better utilisation of the excitons.

11 CHL A FLURESCENCE NDUCTN SMULATN. (a) C =.8 C = V(t)/V max (t)/ max (b) C = C =.5 C = (t) V(t). C =.8.6 C = C =.6. C = C = FG. 7. Simulation results for Chl a fluorescence induction obtained in dark adapted conditions (see Table ), with different values of the connectivity parameter, C =,.5, and : (a) time course of (t)/ max; [inset in panel (a)] time course of (t); (b) time course of V(t)/V max; [inset in panel (b)] time course of V(t). For definition of symbols, see the Glossary. For the normalised fraction of S closed centres, / max curves, small increases at the -step can be observed with increasing values of C. For the V/V max curves the and steps have lower values as C is increased. As can be seen, the connectivity parameter has much more influence on the normalised relative variable fluorescence curves V/V max than on the / max curves. Since 96 (oliot & oliot) the connectivity of S antenna has been measured with fluorescence techniques. According to aillotin (976) the quantum yield of the excitation energy trapping by an open reaction centre, (t), is: (t) = o [ V(t)] () where o is the quantum yield of the excitation energy trapping by an open reaction centre at t =. Therefore, for steady state conditions and a given light intensity, the electron transport rate is proportional to the relative quantum yield,

12 A. STRET ET AL.. C = C =.5 C = C = (adapted).8 C =.5 (t) / o = V(t).6.. C = (ad) C = C = V. C =.5. (t) (t) FG. 8. The relative quantum yield of the exciton energy trapping of an open reaction centre, V(t), as a function of the fraction of closed reaction centres, (t), for different values of the connectivity parameter, C =,.5,,.5 and ; (inset) the differences V =[ V(t)] for C [ V(t)] for C = as a function of the fraction of closed reaction centres, (t), for different values of the connectivity parameter, C =,.5,,.5 and. All the curves are obtained with the input parameters for dark adapted conditions presented in Table, except the curve C = (adapted) which was obtained with an increased value of the rate constant of plastoquinol oxidation, k = 3 s instead of 7 s, and an increased value of the Q exchange reaction, k E = s instead of s. For definition of symbols, see the Glossary. (t) / o = V(t). n Fig. 8 the simulated curves [ V(t)] vs. (t) are shown, for different values of the connectivity constant C. t is evident that a higher degree of connectivity produces an increase in the value of [ V(t)] and therefore, the value of the electron transport. However, we put forward the hypothesis that the connectivity has also a more qualitative goal: the stability of the system in an optimal state relative to the environmental conditions. The difference of the relative quantum yields between the connected and the unconnected case: V =[ V(t)] for C [ V(t)] for C = (5) is a function with a well defined optimum (see Fig. 8 inset) which is linked to the redox buffering capacity of the system. The numerical simulations made for dark adapted samples show that at steady state the system is far away from the optimum. However, if we consider an adapted system (e.g. with an increased value of the rate constant of plastoquinol oxidation, k = 3 s instead of 7 s, and of the Q exchange reaction, k E = s instead of s ) the results show that the system approaches the optimum of this function. A fitting procedure can allow us to determine the best choice of the rate constants, but this will be the objective of another paper. Therefore, we can conclude that the connectivity influences the function of the photosynthetic systems both as activity (the electron transport) and stability of the system towards external perturbations (stress buffering, Krüger et al., 997).

13 CHL A FLURESCENCE NDUCTN SMULATN 3. [Q] =.9.8 [Q] = 6 V(t) V(t)/V max V(t)/V max (a).5 Time (ms) Time (ms) [Q] = 6.75 V(t) D [Q] = 5 nitial Q:QH (6:) (5:) 3 (:). (3:3) (b) 5 (:) FG. 9. Simulated Chl a fluorescence transients in dark adapted conditions (see Table ) for: (a and the inset panel) different number of Q pool molecules: [Q] =, 3,, 5 and 6; (b and the inset panel) different degree of Q pool oxidation: Q:QH =6:, 5:, :, 3:3 and :, (curves 5, respectively). For definition of symbols, see the Glossary. Q L The relative variable fluorescence curves simulated for different number of plastoquinone molecules in the pool are shown in Fig. 9(a). As the plastoquinone exchange reaction is a second order reaction, the rate constant of this reaction, k E, depends on the half time, t /, and the number of Q pool molecules that are initially in the oxidised state, k E = ln /( t / [Q] ). n these simulations we have used the value for the half time of the Q exchange reaction to be ms, independent of the number of the Q molecules in the pool. t can be seen that the number of Q molecules in the pool changes the shape of the V(t)/V max curves, especially in the domain. However, the absolute values of the relative variable fluorescence, V(t), are changed largely in the domain: the greater the number of Q molecules in the pool, the lesser the steady state value of V (e.g. at step, V(t)/ Q =.8 and V(t)/ Q =6.7 a decrease of %) [Fig. 9(a) inset]. At the same time, the steady-state value of the

14 A. STRET ET AL. fraction of closed centres (t) at decreases by 8% as the number of Q molecules in the pool increases from two to six (results not shown). t is obvious that the number of Q pool molecules per S centre in the sample is very important for the fitting of the model with experimental data. As was shown earlier (Lavergne et al., 99; Hsu, 99), there is a high probability that the number of Q molecules which serve one S unit is not the same for all S. However, we do not consider the S and Q heterogeneity in the present work (see the second assumption of the model). t must also be noted, that the area over the fluorescence curve in the linear plot is proportional to the number of Q pool molecules, in agreement with literature predictions (Malkin & Kok, 966) [see the inset in Fig. 9(a)] V(t) 3 D V(t)/V max V(t)/V max V(t) 3 3 D 3 k ox QH (s ) 3 7 (a) k ox QH (s ) 3. 7 (b) FG.. Simulated Chl a fluorescence induction for dark adapted conditions (see Table ) for different values of the plastoquinol oxidation rate constant, kqh ox = 7,, and 3 s (curves, respectively). (a and the inset panel) considering five molecules in Q pool, all oxidised initially; (b and the inset panel) considering six molecules in Q pool, initially five oxidised and one reduced. For definition of symbols, see the Glossary.

15 CHL A FLURESCENCE NDUCTN SMULATN 5 REDX STATE F THE Q L Figure 9(b) shows the results obtained for a Q pool of six molecules with different initial Q:QH ratios (6:; 5:; :; 3:3; and :). n all cases we have used the same value of the rate constant, k E = 5.5 s (resulting from t / = ms, and [Q] = 6). The transients change dramatically in both the and domains (see also the inset). As the initial QH concentration increases, the value of the relative variable fluorescence V(t) becomes higher, and value smaller. n the curve simulated for Q:QH = : the maximum level is already reached by the step and is followed by a subsequent decline [see Fig. 9(b) curve 5]. At the steady state (step ), as the initial QH concentration increases from zero to four, the Q concentration and the fraction of closed S centres decrease by 8 and %, respectively (results not shown). RATE F LASTQUNL XDATN The transients simulated for different values of the plastoquinol oxidation rate constant are presented in Fig.. This reaction takes place at the Cyt b/f level (Hauska et al., 996) which is connected to the S centres by the soluble electron carrier plastocyanin (see Fig. ). Therefore, the ratio between the rate constants of QH oxidation (kqh) ox and Q A reduction (kl) will reflect the balance between the two photosystems. n Fig. the curves obtained with different plastoquinol oxidation rate constants (kqh ox = 7,,, and 3 s ) but with the same initial value of the Q A reduction rate constant (kl = s ) are shown. n Fig. (a) we have considered a Q pool with five molecules, initially all oxidised, and in Fig. (b) a Q pool with six Q molecules, among which five are initially oxidised and one is reduced. n both cases, for higher QH oxidation rates, the relative variable fluorescence increases at the and steps and decreases at the step (see Fig. insets). Moreover, the level is reached more rapidly for high values of the plastoquinol oxidation rate constant. The differences observed in the results presented in Fig. (a) and(b) will be discussed below. N THE AEARANCE F A D D As can be seen in several of the presented figures, the model predicts in certain conditions the appearance of a descending phase between the and steps. The results show that there are several factors which influence its appearance. Firstly, it must be pointed out that the dip D does not appear in the simulations from the models based only on the reactions from the acceptor side of S (Renger & Schulze, 985; aake & Strasser, 99; aake & Schlöder, 99; Hsu, 99, 993; Stirbet & Strasser, 995). We have obtained this dip only on considering the states S n of EC in the model. However, we have shown that although this is a necessary condition, it is not sufficient. The other properties of the system also influence it. The dip D appears and becomes deeper when: () the initial Q :Q ratio of S centres is close to.5:.5 [Fig. 5(f)]; () the number of the molecules in the Q pool is increased [Fig. 9(a)]; (3) the initial number of reduced molecules, QH, in the pool is increased [Fig. 9(b)]; and () the rate constant of plastoquinol oxidation is increased (Fig. ). n the last case, the dip is more pronounced if the Q pool is initially partially reduced (Fig. (b)]. These results are in agreement with the interpretation of the dip as being mainly related to the dynamic equilibrium between the functioning of the two photosystems (see Munday & Govindjee, 969; Schreiber & Vidaver, 97). TRANSENTS F LGHT-ADATED LEAVES A further test of the present model would be achieved if we could simulate the results obtained in experiments in which some external parameters are varied. Here, we have chosen to test the model by simulating transients of light adapted plants (Strasser et al., 995; Stirbet et al., 995). n the light-adapted conditions (see Material and Methods for the experimental conditions) we have assumed that: () initially the Q pool is partially reduced (Q:QH = :); () the degree of connectivity between S units is smaller than for dark adapted conditions (C =.5 instead of.); and (3) the initial rate constant of Q A reduction has a lower value, kl = s instead of s, as in short-term adaptation strategies of plants the absorbed light energy is assumed to be dissipated as heat to a greater extent (Staehelin & van der Staay, 996). n Fig. the curves and are the transients simulated for dark and light adapted conditions, respectively. t can be observed that in the light adapted conditions the relative variable fluorescence reaches its maximum value at the level ( = ), just as in the experimental data (see the inset in Fig. curves and obtained using experimental data presented in Strasser et al., 995). Whether or not this is a unique solution remains to be proven. The above provides a method for testing and provides a means to quantitate and to predict fluorescence transients under various conditions, with known reactions and rate constants in S.

16 6 A. STRET ET AL...8 V(t) V(t)/V max FG.. Time course of the variable Chl a fluorescence induction, V(t)/V max, simulated with input parameters corresponding to the dark adapted and light adapted conditions (see Table ) (curves and, respectively). n the inset, the curves obtained with experimental data presented in Strasser et al. (995) are shown. For definition of symbols, see the Glossary. Conclusions The mathematical model of the first phase of Chl a fluorescence induction in plants presented here utilises the redox reactions at both the acceptor and donor sides of S [see Figs and 3(a) and (b)]. The consistency of the model is supported by the fact that the rate constants of the reactions used in simulations have values close to those reported in the literature (see Table ). The global rate of reduction of Q A was considered to include the light reaction in the model, and we have assumed that its value is two times higher in the S and S states than in the S and S 3 states. artial connectivity between S units [see eqns () (3), and Q non-photochemical quenching (see Appendix) were also needed to explain the experimental data. The simulated fluorescence transient parallel the characteristic steps observed in experimental transients. According to this model, the polyphasic shape of the induction curve is due to the dynamic variations of the concentrations of various redox states of S units [see Fig. (a)]. At the step, Q A Q and Q A Q states predominate. A mixture of different closed states of S units is present at the and steps, the Q A Q H state having the highest concentration. The simulation presented in Fig. shows that even with high light intensity the S units are not all in the closed state when the maximum fluorescence yield is attained, as the reoxidation of QH by S is active. nly in the case of S inhibition can the fraction of S closed centres reach the maximum value, =. t was shown that the connectivity between S antenna influences the function of the photosynthetic systems both quantitatively (enhancing the electron transport) and qualitatively (increasing the stability) (see Fig. 8). The connectivity parameter between S units strongly modifies the shape of the normalised relative variable fluorescence curve, mainly by slowing down the phase [see Figs (b) and 7(b)]. The Q non-photochemical quenching affects in particular the step of the normalised transient, decreasing its value [see Fig. (b)]. The number of plastoquinone molecules per S centre was assumed to be identical for all the centres in this current model (i.e. a homogeneous distribution of Q). This, of course, does not challenge the existence of heterogeneity (Melis & Homann, 975). The simulated transients obtained with different number of molecules in the Q pool have modified shapes, especially in the region [Fig. 9(a) inset]. We have shown that the relationship between the complementary area of the fluorescence transient and the number of plastoquinone molecules is still valid when non-photochemical quenching by the Q-pool is considered. Moreover, the model predicts that the

17 CHL A FLURESCENCE NDUCTN SMULATN 7 initial degree of Q pool oxidation also influences the transient [Fig. 9(b)]. The ratio between S and S activity, expressed here as the ratio between the rate constants of Q A reduction and QH oxidation, also strongly influences the transient. The relative variable fluorescence intensity at the and steps increases as the activity of S is accelerated, and for high S activity (i.e. plastoquinol oxidation rate constant 3 s )itcan reach its maximum value as early as the level [Fig. (b)]. At the same time, the step decreases with the increase of S activity (Figs 9 and insets). The results presented here show that in certain conditions, a descending region of the curve appears between the and steps, usually denoted as dip D. t was not possible to simulate this dip with any of the models that use only the acceptor side of S. Therefore, we can conclude that it is mainly due to the S n states. However, this dip is also influenced by many other factors, such as the ratio between the rates of S and S activities, the degree of S connectivity, the initial Q :Q ratio, the number of molecules in the Q pool, and the initial number of oxidised plastoquinone molecules in the pool. The dip is more pronounced when the relative activity of S is increased, the connectivity parameter C is higher, the initial value of the Q :Q ratio is close to.5:.5, the number of molecules in the Q pool is higher, and the initial number of oxidised plastoquinone molecules in the pool is higher. The simulated curves of fluorescence induction of the light adapted plants exhibit, as in the experimental ones, only the,, and (=) levels (Fig. ). n conclusion, the model presented here allows the possibility to obtain quantitative information from fluorescence transients of leaves, regarding the individual S reactions and the interaction of S with S, which are often difficult to measure directly. The simulations also take into account the donor side of S and the non-photochemical quenching by Q, until now neglected. The next step to be achieved in this work is to provide the fitting of experimental data with the theoretical data obtained through numerical simulation, in order to calculate the values of the input parameters of the model. We expect to establish in this way, data banks for the enormous amount of samples being measured in ecological and environmental investigations. We thank Alaka Srivastava for the experimental data on fluorescence transients of light-adapted leaves used in this paper, and Merope Tsimilli for helpful discussions. This work was supported by Swiss National Foundation (Grant No /). REFERENCES AAKE,E.&SCHLÖDER,.. (99). Modeling the fast fluorescence rise of photosynthesis. ull. Math. iol. 5, 999. AAKE, E.& STRASSER, R.. (99). 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