KINETIC MODEL OF ELECTRON-TRANSPORT REACTIONS IN THYLAKOID MEMBRANES DETERMINING CHLOROPHYLL FLUORESCENCE TRANSIENTS M. Gurmanova 1, P. Chernev 1, I. Zaharieva and V. Goltsev 1 1 Dept. of Biophysics and Radiobiology, Biological Faculty, Sofia University, Sofia, Bulgaria Freie Universität Berlin, FB Physik, Arnimallee 14, D-14195 Berlin, Germany Correspondence to: Vasilij Goltsev E-mail: goltsev@biofac.uni-sofia.bg ABSTRACT The analysis of chlorophyll fluorescence transients is very informative approach for evaluation of the physiological state of the photosynthetic machinery of higher plants. Tsimilli-Mishael and Strasser (008) proposed a system (JIP-test) using the fluorescence transients for calculation of values of energy flows and yields at different stages of the photosynthetic process. In our paper a new model approach is developed for determination of electron transfer rate constants for different sites of the electron transfer chain using the same chlorophyll fluorescence transients. Two kinetic models of the photosynthetic process are constructed. The first one simulates the JIP-test and describes processes determining the three phases of the fluorescence transients during the first second of induction: primary photochemical reaction, electron transfer in the acceptor sides of Photosystem II (PS II) and of PS I. The second model includes most of the components of the electron transfer chain from PS II donor side to PS I. The fitting of the model to real transients allows the determination of rate constant values. Special software Modelyzer for numerical analysis of models is developed. The models are used for analysis of leaves from control plants and others with photosynthetic activity modified as a result of inhibition of electron transport by the herbicide -(,4- dichlorophenil)-1,1-dimethylurea in barley plants wild type and chlorophyll b-less Chlorina f mutant. A good correlation between model values of rate constants with JIP-test results is observed. Keyword: JIP-test, Mathematical modeling, Photosystem II, Variable chlorophyll fluorescence Abbreviations: B, relative concentration of highly fluorescent (closed) PS II reaction centers; DCMU, diuron, - (,4-dichlorophenil)-1,1-dimethylurea; PQ, Plastoquinone; PS I and PS II, Photosystems I and II Introduction The evaluation of behaviour of the living systems in stress conditions requires application of experimental methods that analyse the physiological state of the organisms without disturbing their integrity. Photosynthesis is the most sensitive to the changes in environmental conditions process (9) and often is used as an informative indicator of whole plant states. During the last decade as the most perspective methods for in vivo and in situ monitoring of photosynthetic process emerged prompt and delayed chlorophyll fluorescence (, 5, 1) that is native emission of plants and provide on line information for photosynthetic reactions on molecular level. Strasser and co-authors (10, 1) developed an approach for analysis of the chlorophyll a fluorescence transients (JIP-test) to obtain the quantitative information about energetic flows and photosynthesis effectiveness. Another very useful approach for quantification of the luminescence data supposes a kinetic description of photosynthetic reactions and comparison of the model data with the experimental curves (1,, 5, 6). In this paper two kinetic models of photosynthetic electron transfer in both photosystems are constructed for simulation of the changes in chlorophyll fluorescence dynamics during dark to light adaptation of photosynthetic machinery. Using specially developed for numerical analysis of the mathematical models software, Modelyzer (1), the parameters of the model were fitted to the experimental data from fluorescence transients in barley leaves (wild type and Chlorina f mutant with diminished PS II antennae size), the control ones and those, treated with photosystem II herbicide, SPECIAL EDITION/ON-LINE 61 10 YEARS OF ACADEMIC EDUCATION IN BIOLOGY
diuron. Materials and methods All measurements were done with the primary leaves of 8 days old barley plants (Hordeum vulgare), wild type and Chlorina f mutant, grown in a growth chamber at 0 C as a hydroponics culture on Knopp solution. The light regime was 1 h dark / 1 h light (continuous white irradiation of 50 μmol.m -.s -1 ). The measurements were done in the light growing phase after 1-h dark adaptation period. Chlorophyll fluorescence induction curves with a recording time of 1 s were obtained by the Handy-PEA (Plant Efficiency Analyzer, Hansatech Instruments Ltd., England) at irradiation of 000 μmol.m -.s -1. Fluorescence was collected from the adaxial leaf side, approximately cm from the leaf tip. Plants were treated with herbicide diuron or DCMU (-(,4- dichlorophenil)-1,1-dimethylurea, Sigma) through the roots by addition of diuron in final concentration 10 µm in nutrient solution where plants were incubated 4 h before fluorescence measurements. The model differential equations were constructed and numerically solved by a computer program Modelyzer described earlier (1). Results and Discussion Model of fluorescence transients Photoinduced chlorophyll fluorescence grows during the first one second of illumination by actinic light and passes three characteristic steps denoted as OJIP. A phenomenological model (JIP-test) that describes fluorescence transients was developed by Strasser and coworkers (10, 1) to determine a set of important quantitative photosyntetic parameters. Using the values of some characteristic points of OJIP curve the energetic fluxes (ABS absorbed energy flux; TR 0 trapped in PSII reaction energy; ET 0 electron flux from Q A to quinone acceptor pool between the photosystems; RE 0 electron flux to PSI acceptors) and the effectiveness of energy transformation at different stages of photosynthetic process (ϕ Po yield of the primary photochemical reaction in PSII; ψ 0 yield of the electron transfer trough PSII and PSI (δ 0 ) acceptors) can be calculated. In addition to the information obtained by JIP-test, the values of the rate constants of the electron transport reactions between electron carriers can be provided by dynamic mathematical models. We constructed a model that describes photosynthetic reactions influencing the chlorophyll fluorescence yield and determining the shape of the fluorescence curve during the transition from dark to light-adopted state. The model includes components as follows: P 680, P 700 photochemically active chlorophylls of PSII and PSI reaction centers; Z, Q A electron carriers in donor and acceptor side of PSII; PQ, PC plastoquinone and plastocyanine carriers. A linear photoinduced electron transfer is presented model in the followed scheme (Fig. 1) Fig. 1. Scheme of photosynthetic electron transfer chain and redox reactions. Arrows show the direction of electron transport between carriers and k i are rate constants of forward and k -i of backward redox reactions The electron carriers PQ, PC and P 700 are independent components of the electron transfer chain and their redox reactions were described with second order equations. PS II electron carriers function as a complex ZP 680 O A, and should be analyzed as a separate unit and electron transport (8) as a transition between different redox states according to the scheme (Fig. ): Fig.. Scheme of redox reactions in PS II complex of electron carriers. Black arrows show the direction of electron transport between carriers and k i are rate constants as in Fig. 1. With red arrows are marked photoinduced primary photochemical reactions and recombinations of primary dipole. With symbols ( + ) and ( ) after letters are denoted oxidized and reduced states of corresponding carriers. In the model the relative concentrations of redox states of the complex are evaluated. The total concentration of reaction centers is accepted equal to 1. Keeping in mind that the sum of all states is constant, i.e. = 1 ( x + x + x + x + x + x x ) (1) x0 1 4 5 6 + 7 the dynamics of PS II reaction center can be analyzed by describing of the rates of photoinduced redox reaction by the following system of 7 differential equations: 6 10 YEARS OF ACADEMIC EDUCATION IN BIOLOGY SPECIAL EDITION/ON-LINE
dx 1 = k0x1 + k 0 1 x dx dx dx ( ( x1 + x + x + x4 + x5 + x6 + )) k 1x1 + k1x kx1 + k k x1 + k 5 = k 0x + k0x k1x + k 1x1 k x + k x 6 = k 0 x + k 0 x k x + k x 4 = k 0 x4 + k0 x5 k x4 + k dx5 = k0 x5 + k dx6 = k 0 x4 k 1x5 + k1x6 k x5 + 7 ( 1 ( x + x + x + x + x + x + x )) 1 k x 1 4 5 6 7 ( 1 ( x1 + x + x + x4 + x5 + x6 + )) k x6 k x 0 x6 + k0 k1x6 + k 1x5 k x6 + k + d = k0 + k 0 x6 k + kx1 k + k x () () (4) (5) (6) (7) (8) Here variables x 1 x 7 are partial concentrations of PS II reaction center in different redox states as denoted in Fig.. dpq. H ( x + x + x + x ) PQ.H ( 1 PC) = k 4 5 6 7 k4 dpc = PQ.H k4 5 size dpsi ( 1 PC) PC k ( PSI PSI) = size ( PSI PSI) PC k 5 Here k is a function of the oxidized plastoquinone (PQ) molecules concentration: k = k pq *(1-[PQ.H ]), and k pq is bimolecular rate constant of PQ reduction by PS II acceptors. The intensity of the variable part of the chlorophyll fluorescence is determined by the presence of primary quinine acceptor Q A in reduced state in PS II reaction centers that contain non oxidized form of primary donor (P 680 ). These complexes are ZPQ A and Z + PQ A, and their relative concentrations are x 4 and x 5, correspondingly. Calculating the fluorescence intensity, the possibility of energy migration between antennae complexes of closed and opened photosystems should be kept in mind. That is why the variable connectivity (Conn) is introduced as a function of the relative concentration of highly fluorescent (closed) reaction centers (B). This variable is dependent on parameters grouping or connectivity introduced by (4, 11) and reflects the probability for excitation energy transfer between the antennae of several PS II units (p G ) (1): The rest reactions can be described by differential equations including second order terms: (9) (10) (11) Conn = p G B (1-B) Then, the total fluorescence is the sum of the fluorescence emitted by the antenna complex of the PS II units with open (F op ) and those with closed (F cl ) reaction centers and keeping in mind the connectivity, we get: op cl Ft = Light _ Int ( F (( 1 B) + Conn) + F ( B Conn) ) (1) where Light_Int represents the rate of excitation formation in PS II antennae complexes. Numerical analysis of the model The model was validated by specialized software Modelyzer (1). For the numerical integration, the program uses a Runge- Kuta algorithm of order 4 with a variable step size. For validation, the program fits the model parameters by comparing the model curves of calculated fluorescence function to the experimental ones. For the non-linear function minimization, it uses a simulated annealing algorithm with the downhill simplex method of Nelder and Mead, or a modified version of the Powell s method in multiple dimensions (7). SPECIAL EDITION/ON-LINE 6 10 YEARS OF ACADEMIC EDUCATION IN BIOLOGY
Chlorophyll fluorescence, rel.u. 4000 500 000 500 000 1500 1000 Experiment - WT Model - WT Experiment - f Model - f A Residuals WT Residuals f 0 0 10 0-10 -0 Residuals, rel.u. Chlorophyll fluorescence, rel.u. 4500 4000 500 000 500 000 1500 1000 Experiment - WT Model - WT Experiment - f Model - f B Residuals WT Residuals f 0 0 10 0-10 -0-0 Residuals, rel.u. 500 0.01 0.1 1 10 100 1000-0 500 0.01 0.1 1 10 100 1000-40 Induction time, ms Induction time, ms Fig.. Results of the fitting procedure for the parameters of the mathematical model described on Fig. 1 to experimental data of chlorophyll fluorescence transients in the leaves of wild type (red points) and Chlorina f mutant (blue points) of 8 day-old control barley plants (A) or treated 4 h with 10 µm solution of -(,4-dichlorophenil)-1,1-dimethylurea. Chlorophyll fluorescence (points) was measured in min dark adapted leaves illuminated by 000 µmol.m -.s -1 red light. Continuous lines represent best fits of the model (Eqs. 1 11). On the right scale the residuals for corresponding fits are presented. TABLE 1 Comparison of the results of JIP-test with values of parameters of the model presented in Fig. 1 (Model 1) and the complete model including Q B electron carrier (Model ) wild type Chlorina f wild type Chlorina f Parameter control diuron control diuron Parameter control diuron control diuron ABS/RC.15 5..1 5.81 Light_Int 4.19 8.17.67.0 TRo/RC.4. 1.67.47 k 1 49.51 5.15 44.18 1.8 ETo/RC 1.8 0.08 1. 0.4 k a.64 0.015.61 4E-09 REo/RC 0.0 0.0 0.40 0.09 k b.51.18. 1.9 Sm 11.4.57 4.77 7.5 k pq 0.7 5.8 0.14 0.77 PhiPo 0.77 0.61 0.7 0.4 k 6 PS I size.04.57 1.4 0.01 PhiEo 0.44 0.0 0.5 0.04 pqsize 19.74 0.06 7.9 4.5 PhiRo 0.10 0.01 0.17 0.0 pg 0.9 0.5 0.94 0.55 Light_Int.95 6.70 1.45.94 k 1 9.51 8.46 1.19 5.1 k pq 0.4 0.00 0.18 0.001 k 5 PS I size 0.156 0.191 0.146 0.008 pqsize.08 4.56 7.7.46 pg 0.7 0.57 0.06 0.1 JIP Model 1 Model The model parameters are fitted to chlorophyll fluorescence transients for barley leaves in wild type plants and in Chlorina f mutants (Fig. A). The averaged relative fitting error was calculated by formulae: = Δ x, where x i are i Er n the variations between experimental and calculated from the model values of fluorescence. For data presented on Fig. the errors are about 5 10-5. Some of the model parameters are compared with the values of calculated JIP-test parameters (see Table 1). There is a good correlation in parameters, reflecting the effective PS II antennae size (ABS/RC in JIP-test and Light_Int in Model 64 10 YEARS OF ACADEMIC EDUCATION IN BIOLOGY SPECIAL EDITION/ON-LINE
1), the rate of Q A reoxidation (ETo/RC and k pq, correspondingly) in analyzed variants. The other model parameters showed a deviation to some extent from those of JIP-test. In JIP-test the Q A reoxidation was presented by electron flow in PS II acceptor side without detailed description of the electron carriers. That is why in the Model 1 we simulated the JIP-test and the electron flow in PS II acceptor side was described only by Q A and PQ. Evidently, such a description simulates well the shape of fluorescence transient (Fig. ) but does not allow precise determination of all rate constants. In the complete version of the model (Model ) we included in the complex of electron carriers the second quinon, Q B, located between Q A and PQ. In this case the dynamics of the complex can be expressed by the system of differential equations instead 7 as in Model 1. The numerical analysis of this model (see Table 1) shows better fitting results (lower level of residuals, see Fig. 4) than Model 1 and correlation with the parameters of JIP-test and provide additional quantitative information (for example, the rate constant of electron transfer in PS II donor side, k 1 ). It is interesting to note that diuron suppress the Q A reoxidation by Q B (rate constant k a ), but does not by Q B (rate constant k b ) In conclusion, the comlpete model (Model ) adequate describes photosynthetic reaction that determines variable chlorophyll fluorescence changes and this model analysis can be useful for evaluation of physiological state of plants in natural conditions. Fig. 4. Results of the fitting procedure for the parameters of the mathematical model including Q B in addition to reactions described in Fig. 1. Experimental conditions as in Fig.. Acknowledgments We thank the Bulgarian National Science Fund, Project DO 0-17 / 15.1.008 for the financial support. REFERENCES 1. Chernev P., Goltsev V., Zaharieva I., Strasser R.J. (006) Ecol. Enger. Environ. Prot. 5, 19-9.. Goltsev V., Chernev P., Zaharieva I., Lambrev P., Strasser R.J. (005) Photosynth. Res. 84, 09-15.. Goltsev V.N., Yordanov I.T. (1997) Photosynthetica,, 571-586. 4. Joliot P., Joliot A. (1964) CR Acad.Sci.Paris, 58, 46-465. 5. Lazar D. (1999) Biochim.Biophys.Acta, 141, 1-8. 6. Lazar D., Jablonsky J. (009) J.Theor.Biol. 57, 60 69. 7. Press W., S. Teukolsky, W. Vetterling, B. Flannery (199) Numerical Recipes in C++: The Art of Scientific Computing, Cambridge University Press 8. Rubin A.B., V.P. Shinkarev (1984) Electron transport in biological systems, Nauka, Moscow (In Russ.). 9. Saibo N.J.M., Lourenço T., Oliveira M.M. (009) Ann. Bot., 10, 609-6. 10. Strasser R, Srivastava A, Tsimilli-Michael M. (004) In: Chlorophyll a fluorescence: a signature of photosyn- SPECIAL EDITION/ON-LINE 65 10 YEARS OF ACADEMIC EDUCATION IN BIOLOGY
thesis. (Papageorgiou G, Govindjee, eds.) The Netherlands: Kluwer Academic Publishers; 1 6. 11. Strasser R.J. (1978) In: Chloroplast Development (G. Akoyunoglou, Ed.) Elsevier, North Holland, 51-54. 1. Strasser R.J. (1981) In: Photosynthesis III. Structure and Molecular Organization of the Photosynthetic Apparatus (G. Akoyunoglou, Ed.) Balaban International Science Services, Philadelphia, 77-77. 1. Tsimilli-Michael M., Strasser R. (008) In: Mycorrhiza: State of theart, genetic sand molecular biology, ecofunction, biotechnology, eco-physiology, structure and systematics (Varma A., ed.). rd ed., Springer, 679 70. 66 10 YEARS OF ACADEMIC EDUCATION IN BIOLOGY SPECIAL EDITION/ON-LINE