Electron and proton transport in chloroplasts taking into account lateral heterogeneity of thylakoids. Mathematical model]

A mathematical model of a chloroplast was constructed, which takes into account the inhomogeneous distribution of complexes of photosystems I and II between granal and intergranal thylakoids. The structural and functional complexes of photosystems I and II, which are localized in intergranal and granal thylakoids, respectively, and the b/f complex, which is uniformly distributed in thylakoid membranes, are assumed to be immobile. The interactions between spatially distant electron transport complexes are provided by plastoquinone and plastocyanine, which diffuse in the thylakoid membrane and intrathylakoid space, respectively. The main stages of proton transport associated with the functioning of photosystem II and oxidation-reduction transformations of plastoquinone are considered. The model takes into account the interactions of protons with membrane-bound buffer groups, the lateral diffusion of hydrogen ions in the intrathylakoid space and in the lumen between adjacent granal thylakoids, and the transmembrane proton transport associated with the function of ATP synthase and passive leakage of protons from thylakoids outside. The numerical integration of two systems of differential equations describing the behavior of some variables in two different regions: granal and intergranal thylakoids was performed. The model describes adequately the kinetics of processes being studied and predicts the occurrence of inhomogeneous lateral profiles of proton potentials and redox state of electron carriers. Modeling the electron and proton transport with allowance for the topological features of chloroplasts (lateral heterogeneity of thylakoids) is important for correct interpretation of "power-flux" interactions and the experimentally measured kinetic parameters averaged over the entire spatially inhomogeneous thylakoid system.     

Bidirectional electron transfer in photosystem I: replacement of the symmetry-breaking tryptophan close to the PsaB-bound phylloquinone A1B with a glycine residue alters the redox properties of A1B and blocks forward electron transfer at cryogenic temperatures

A conserved tryptophan residue located between the A(1B) and F(X) redox centres on the PsaB side of the Photosystem I reaction centre has been mutated to a glycine in Chlamydomonas reinhardtii, thereby matching the conserved residue found in the equivalent position on the PsaA side. This mutant (PsaB:W669G) was studied using EPR spectroscopy with a view to understanding the molecular basis of the reported kinetic differences in forward electron transfer from the A(1A) and the A(1B) phyllo(semi)quinones. The kinetics of A(1)(-) reoxidation due to forward electron transfer or charge recombination were measured by electron spin echo spectroscopy at 265 K and 100 K, respectively. At 265 K, the reoxidation kinetics are considerably lengthened in the mutant in comparison to the wild-type. Under conditions in which F(X) is initially oxidised the kinetics of charge recombination at 100 K are found to be biphasic in the mutant while they are substantially monophasic in the wild-type. Pre-reduction of F(X) leads to biphasic kinetics in the wild-type, but does not alter the already biphasic kinetic properties of the PsaB:W669G mutant. Reduction of the [4Fe-4S] clusters F(A) and F(B) by illumination at 15 K is suppressed in the mutant. The results provide further support for the bi-directional model of electron transfer in Photosystem I of C. reinhardtii, and indicate that the replacement of the tryptophan residue with glycine mainly affects the redox properties of the PsaB bound phylloquinone A(1B).     

Kinetics of charge separation and A0- --> A1 electron transfer in photosystem I reaction centers

The charge separation P700*A(0) --> P700(+)A(0)(-) and the subsequent electron transfer from the primary to secondary electron acceptor have been studied by subtracting absorption difference profiles for cyanobacterial photosystem I (PS I) complexes with open and closed reaction centers. Samples were excited at 660 nm, which lies toward the blue edge of the core antenna absorption spectrum. The resulting PS I kinetics were analyzed in terms of the relevant P700, P700(+), A(0), and A(0)(-) absorption spectra. In our kinetic model, the radical pair P700(+)A(0)(-) forms with 1.3 ps rise kinetics after creation of electronically excited P700*. The formation of A(1)(-) via electron transfer from A(0)(-) requires approximately 13 ps. The kinetics of the latter step are appreciably faster than previously estimated by other groups (20--50 ps).     

Regulation of electron-transport pathways in cells of Chlamydomonas reinhardtii under stress conditions

The kinetics of interactions between electron-transport pathways in the thylakoid membrane was examined. A mathematical model was proposed to describe the kinetics of redox transitions in photosystem II, proton concentration changes in the chloroplast stroma, and the plastoquinone pool reduction due to photosynthetic and chlororespiratory pathways. A kinetic mechanism is considered that redirects electron flows between photosynthetic and chlororespiratory pathways in response to the increased NADPH content under mineral deficiency. According to the simulation model, the electron transport flows via different routes are switched over in a stepwise manner. The results of numerical simulations are qualitatively consistent with experimental data for Chlamydomonas reinhardtii cells subjected to mineral deprivation.     

Assignment of a kinetic component to electron transfer between iron-sulfur clusters F(X) and F(A/B) of Photosystem I

We studied the kinetics of reoxidation of the phylloquinones in Chlamydomonas reinhardtii Photosystem I using site-directed mutations in the PhQ(A)-binding site and of the residues serving as the axial ligand to ec3(A) and ec3(B) chlorophylls. In wild type PS I, these kinetics are biphasic, and mutations in the binding region of PhQ(A) induced a specific slowing down of the slow component. This slowing allowed detection of a previously unobserved 180-ns phase having spectral characteristics that differ from electron transfer between phylloquinones and F(X). The new kinetic phase thus reflects a different reaction that we ascribe to oxidation of F(X)(-) by the F(A/B) FeS clusters. These absorption changes partly account for the differences between the spectra associated with the two kinetic components assigned to phylloquinone reoxidation. In the mutant in which the axial ligand to ec3(A) (PsaA-Met688) was targeted, about 25% of charge separations ended in P(700)(+)A(0)(-) charge recombination; no such recombination was detected in the B-side symmetric mutant. Despite significant changes in the amplitude of the components ascribed to phylloquinone reoxidation in the two mutants, the overall nanosecond absorption changes were similar to the wild type. This suggests that these absorption changes are similar for the two different phylloquinones and that part of the differences between the decay-associated spectra of the two components reflect a contribution from different electron acceptors, i.e. from an inter-FeS cluster electron transfer.     

Modeling of primary photosynthetic processes using the kinetic Monte Carlo method

Processes that occur in the ensemble of photosynthetic electron transport systems have been modeled using a kinetic Monte Carlo method. The size of a simulated ensemble (3–5 million elementary photosynthetic chains) corresponds to the number of photosynthetic reaction centers in a plant cell. The method enables one to modify the structure of a model system according to different concepts of the organization of processes in a photosynthetic membrane. Using this model, the experimental kinetics of the chlorophyll fluorescence induction associated with the Photosystem II and the redox transformations of a photoactive pigment of the Photosystem I have been successfully reproduced. The model was verified by comparing the calculated fluorescence induction curves to experimental curves, obtained in the presence of various photosynthesis inhibitors and under temperature inactivation of the Photosystem II donor side.     

Regulation of electron transfer by the quinone pool

Strong evidence for a random collisional mechanism for ubiquinone-mediated electron transfer is provided by the characteristic kinetic properties of respiratory chains originally explored by Kröger, A., and Klingenberg, M. (1973),Eur. J. Biochem. 34, 313–323. A kinetic model which leads to this so-called simple Q-pool behavior has been described and we use this in reviewing evidence that electron transfer is diffusion-controlled as well as diffusion-coupled. We also consider mechanisms by which the kinetics of electron transfer might deviate from simple Q-pool behavior and how these might be implicated in the regulation of electron transport.     

Simulation of chlorophyll fluorescence rise and decay kinetics,and P<Subscript>700</Subscript>-related absorbance changes by using a rule-based kinetic Monte-Carlo method

A model of primary photosynthetic reactions in the thylakoid membrane was developed and its validity was tested by simulating three types of experimental kinetic curves: (1) the light-induced chlorophyll a fluorescence rise (OJIP transients) reflecting the stepwise transition of the photosynthetic electron transport chain from the oxidized to the fully reduced state; (2) the dark relaxation of the flash-induced fluorescence yield attributed to the Q_A^? oxidation kinetics in PSII; and (3) the light-induced absorbance changes near 820 or 705 nm assigned to the redox transitions of P₇₀₀ in PSI. A model was implemented by using a rule-based kinetic Monte-Carlo method and verified by simulating experimental curves under different treatments including photosynthetic inhibitors, heat stress, anaerobic conditions, and very high light intensity.     

Autocatalytic conversion of recombinant prion proteins displays a species barrier

The most unorthodox feature of the prion disease is the existence of an abnormal infectious isoform of the prion protein, PrP(Sc). According to the "protein-only" hypothesis, PrP(Sc) propagates its abnormal conformation in an autocatalytic manner using the normal isoform, PrP(C), as a substrate. Because autocatalytic conversion is considered a key element of prion replication, in this study I tested whether in vitro conversion of recombinant PrP into abnormal isoform displays specific features of an autocatalytic process. I found that recombinant human PrP formed two distinct beta-sheet rich isoforms, the beta-oligomer and the amyloid fibrils. The kinetics of the fibrils formation measured at different pH values were consistent with a model in which the beta-oligomer was not on the kinetic pathway to the fibrillar form. As judged by electron microscopy, an acidic pH favored to the long fibrils, whereas short fibrils morphologically similar to "prion rods" were formed at neutral pH. At neutral pH the conversion to the fibrils can be seeded with small aliquots of preformed fibrils. As small as 0.001% aliquot displayed seeding activity. The conversion of human PrP was seeded with high efficacy only with the preformed fibrils of human but not mouse PrP and vice versa. These studies illustrate that in vitro conversion of recombinant PrP displays specific features of an autocatalytic process and mimics the transmission barrier of prion propagation observed in vivo. I speculate that this model can be used as a rapid assay for assessing the intrinsic propensities of prion transmission between different species.     

The kinetics of granulopoiesis in long-term mouse bone marrow culture. Part II

A mathematical model of mouse granulopoiesis in long-term bone marrow culture was constructed, based on established in vivo cell kinetic parameters. We applied the model to the cell kinetic experiment presented in Part I. Comparing model-predicted cell kinetics with the experimental data led to iterative testing of several hypotheses. In the final model, the cell kinetics of intact tissue culture flasks were reconstructed, using the experimental data from 10 days of tube culture. Among other things, our analysis suggests that the parameters of normal in vivo granulopoiesis apply to bone marrow culture.     

Electron transfer through the acceptor side of photosystem I: Interaction with exogenous acceptors and molecular oxygen

This review considers the state-of-the-art on mechanisms and alternative pathways of electron transfer in photosynthetic electron transport chains of chloroplasts and cyanobacteria. The mechanisms of electron transport control between photosystems (PS) I and II and the Calvin–Benson cycle are considered. The redistribution of electron fluxes between the noncyclic, cyclic, and pseudocyclic pathways plays an important role in the regulation of photosynthesis. Mathematical modeling of light-induced electron transport processes is considered. Particular attention is given to the electron transfer reactions on the acceptor side of PS I and to interactions of PS I with exogenous acceptors, including molecular oxygen. A kinetic model of PS I and its interaction with exogenous electron acceptors has been developed. This model is based on experimental kinetics of charge recombination in isolated PS I. Kinetic and thermodynamic parameters of the electron transfer reactions in PS I are scrutinized. The free energies of electron transfer between quinone acceptors A_1A/A_1B in the symmetric redox cofactor branches of PS I and iron–sulfur clusters F_X, F_A, and F_B have been estimated. The second-order rate constants of electron transfer from PS I to external acceptors have been determined. The data suggest that byproduct formation of superoxide radical in PS I due to the reduction of molecular oxygen in the A1 site (Mehler reaction) can exceed 0.3% of the total electron flux in PS I.     

Functional role of vitamin K in photosystem I of the cyanobacterium Synechocystis 6803

The function of vitamin K1 in the primary electron-transfer processes of photosystem I (PS I) was investigated in the cyanobacterium Synechocystis 6803. A preparation of purified PS I was found to contain two vitamin K1's per reaction center. One vitamin K1 was removed by extraction with hexane, and further extraction using hexane including 0.3% methanol resulted in a preparation devoid of vitamin K1. The hexane-extracted PS I was functional in the photoreduction of NADP+, but the PS I after extraction using hexane-methanol was totally inactive. Activity was restored by using exogenous vitamin K1 plus the hexane extract. Vitamin K3 would not substitute. The room temperature recombination kinetics of the PS I extracted with hexane were not significantly modified. However, following the removal of both vitamin K1's, the 20-ms recombination between P-700+ and P-430- was replaced by a dominant relaxation (t 1/2 = 30 ns) due to recombination of the primary biradical P-700+ A0- and a slower component originating from the P-700 triplet. This kinetic behavior was consistent with an interruption of forward electron transfer to the acceptor A1. Addition of either vitamin K1 or vitamin K3 to such preparations resulted in restoration of the slow kinetic phase (greater than 2 ms), indicating significant competition by the two exogenous quinones for electron transfer from A0-. In the case of vitamin K3, this change in the kinetics induced by vitamin K1, suggesting successful reconstitution of the acceptor site A1. These data support the hypothesis that acceptor A1 is vitamin K1 and is a component of the electron-transfer pathway for NADP+ reduction.     

Analysis of Ter-Ter enzyme kinetic mechanisms by computer simulation of isotope exchange at chemical equilibrium: development and application of ISOTER, a personal-computer-based program

A convenient, personal-computer-based program has been developed that allows simulation of isotopic exchange kinetics at chemical equilibrium catalyzed by a three reactant-three product (TerTer) enzyme system: A + B + C integral of P + Q + R. This program, ISOTER, utilizes a rapid algebraic method to calculate the exchange rate between any reactant-product pair as a function of the substrate concentration and avoids altogether the necessity of deriving an explicit (but cumbersome and impractical) equation for exchange rate. ISOTER was used to generate model saturation patterns for 16 different TerTer kinetic mechanisms, varying different combinations of reactant-product pairs in constant ratio at equilibrium: [all substrates], [A, P], [B, Q], and [C, R], while holding the nonvaried components constant. These model studies indicate that virtually every one of these mechanisms can be distinguished from the others. In addition, ISOTER has been used to fit multiple sets of experimental data for Escherichia coli glutamine synthetase, which produced a set of rate constants consistent with the previously proposed "preferred order random" kinetic mechanism.     

Butler-Volmer-Monod model for describing bio-anode polarization curves

A kinetic model of the bio-anode was developed based on a simple representation of the underlying biochemical conversions as described by enzyme kinetics, and electron transfer reactions as described by the Butler-Volmer electron transfer kinetics. This Butler-Volmer-Monod model was well able to describe the measured bio-anode polarization curves. The Butler-Volmer-Monod model was compared to the Nernst-Monod model described the experimental data significantly better. The Butler-Volmer-Monod model has the Nernst-Monod model as its full electrochemically reversible limit. Contrary to the Nernst-Monod model, the Butler-Volmer-Monod model predicts zero current at equilibrium potential. Besides, the Butler-Volmer-Monod model predicts that the apparent Monod constant is dependent on anode potential, which was supported by experimental results.     

Near-IR absorbance changes and electrogenic reactions in the microsecond-to-second time domain in Photosystem I.

The back-reaction kinetics in Photosystem I (PS I) were studied on the microsecond-to-s time scale in cyanobacterial preparations, which differed in the number of iron-sulfur clusters to assess the contributions of particular components to the reduction of P700+. In membrane fragments and in trimeric P700-FA/FB complexes, the major contribution to the absorbance change at 820 nm (delta A820) was the back-reaction of FA- and/or FB- with lifetimes of approximately 10 and 80 ms (approximately 10% and 40% relative amplitude). The decay of photoinduced electric potential (delta psi) across a membrane with directionally incorporated P700-FA/FB complexes had similar kinetics. HgCl2-treated PS I complexes, which contain FA but no FB, retain both of these kinetic components, indicating that neither can be assigned uniquely to a specific acceptor. These results suggest that FA- reduces P700+ directly and argue for a rapid electron equilibration between FA and FB, which would eliminate their kinetic distinction in a back-reaction. In PsaC-depleted P700-Fx cores, as well as in P700-FA/FB complexes with chemically reduced FA and FB, the major contribution to the delta A820 and the delta psi decay is a biphasic back-reaction of F-X (approximately 400 microseconds and 1.5 ms) with some contribution from A-1 (approximately 10 microseconds and 100 microseconds), the latter of which is variable depending on experimental conditions. The delta A820 decay in a P700-A1 core devoid of all iron-sulfur clusters comprises two phases with lifetimes of 10 microseconds and 130 microseconds (2.7:1 ratio). The biexponential back-reaction kinetics found for each of the electron acceptors may be related to existence of different conformational states of the PS I complex. In all preparations studied, excitation at 532 nm with flash energies exceeding 10 mJ gives rise to formation of antenna 3Chl, which also contributes to delta A820 decay on the tens-of-microsecond time scale. A distinction between delta A820 components related to back-reactions and to 3Chl decay can be made by analysis of flash saturation dependencies and by measurements of kinetics with preoxidized P700.     

Variable velocity liquid flow EPR applied to submillisecond protein folding

We have developed a variable velocity, rapid-mix, continuous-flow method for observing and delineating kinetics by dielectric resonator-based electron paramagnetic resonance (EPR). The technology opens a new facet for kinetic study of radicals in liquid at submillisecond time resolution. The EPR system (after Sienkiewicz, A., K. Qu, and C. P. Scholes. 1994. Rev. Sci. Instrum. 65:68-74) accommodated a miniature quartz capillary mixer with an approximately 0.5 microliter delivery volume to the midpoint of the EPR-active zone. The flow velocity was varied in a preprogrammed manner, giving a minimum delivery time of approximately 150 microseconds. The mixing was efficient, and we constructed kinetics in the 0.15-2. 1-ms time range by plotting the continuous wave EPR signal taken during flow versus the reciprocal of flow velocity. We followed the refolding kinetics of iso-1-cytochrome c spin-labeled at Cysteine 102. At 20 degrees C, upon dilution of guanidinium hydrochloride denaturant, a fast phase of refolding was resolved with an exponential time constant of 0.12 ms, which was consistent with the "burst" phase observed by optically detected flow techniques. At 7 degrees C the kinetic refolding time of this phase increased to 0.5 ms.     

Kinetic modeling of electron transfer reactions in photosystem I complexes of various structures with substituted quinone acceptors

The reduction kinetics of the photo-oxidized primary electron donor P₇₀₀ in photosystem I (PS I) complexes from cyanobacteria Synechocystis sp. PCC 6803 were analyzed within the kinetic model, which considers electron transfer (ET) reactions between P₇₀₀, secondary quinone acceptor A₁, iron-sulfur clusters and external electron donor and acceptors – methylviologen (MV), 2,3-dichloro-naphthoquinone (Cl₂NQ) and oxygen. PS I complexes containing various quinones in the A₁-binding site (phylloquinone PhQ, plastoquinone-9 PQ and Cl₂NQ) as well as F _X-core complexes, depleted of terminal iron–sulfur F _A/F _B clusters, were studied. The acceleration of charge recombination in F _X-core complexes by PhQ/PQ substitution indicates that backward ET from the iron–sulfur clusters involves quinone in the A₁-binding site. The kinetic parameters of ET reactions were obtained by global fitting of the P₇₀₀ ⁺ reduction with the kinetic model. The free energy gap ΔG ₀ between F _X and F _A/F _B clusters was estimated as ?130 meV. The driving force of ET from A₁ to F _X was determined as ?50 and ?220 meV for PhQ in the A and B cofactor branches, respectively. For PQ in A_1A-site, this reaction was found to be endergonic (ΔG ₀?=?+75 meV). The interaction of PS I with external acceptors was quantitatively described in terms of Michaelis–Menten kinetics. The second-order rate constants of ET from F _A/F _B, F _X and Cl₂NQ in the A₁-site of PS I to external acceptors were estimated. The side production of superoxide radical in the A₁-site by oxygen reduction via the Mehler reaction might comprise ≥0.3% of the total electron flow in PS I.     

Exploring "one-shot" kinetics and small molecule analysis using the ProteOn XPR36 array biosensor

A ProteOn XPR36 parallel array biosensor was used to characterize the binding kinetics of a set of small molecule/enzyme interactions. Using one injection with the ProteOn's crisscrossing flow path system, we collected response data for six different concentrations of each analyte over six different target protein surfaces. This "one-shot" approach to kinetic analysis significantly improves throughput while generating high-quality data even for low-molecular-mass analytes. We found that the affinities determined for nine sulfonamide-based inhibitors of the enzyme carbonic anhydrase II were highly correlated with the values determined using isothermal titration calorimetry. We also measured the temperature dependence (from 15 to 35 degrees C) of the kinetics for four of the inhibitor/enzyme interactions. Our results illustrate the potential of this new parallel-processing biosensor to increase the speed of kinetic analysis in drug discovery and expand the applications of real-time protein interaction arrays.