Herbicide-induced changes in charge recombination and redox potential of Q(A) in the T4 mutant of Blastochloris viridis.

To gain new insights into the function of photosystem II (PSII) herbicides DCMU (a urea herbicide) and bromoxynil (a phenolic herbicide), we have studied their effects in a better understood system, the bacterial photosynthetic reaction center of the terbutryn-resistant mutant T4 of Blastochloris (Bl.) viridis. This mutant is uniquely sensitive to these herbicides. We have used redox potentiometry and time-resolved absorption spectroscopy in the nanosecond and microsecond time scale. At room temperature the P(+)(*)Q(A)(-)(*) charge recombination in the presence of bromoxynil was faster than in the presence of DCMU. Two phases of P(+)(*)Q(A)(-)(*) recombination were observed. In accordance with the literature, the two phases were attributed to two different populations of reaction centers. Although the herbicides did induce small differences in the activation barriers of the charge recombination reactions, these did not explain the large herbicide-induced differences in the kinetics at ambient temperature. Instead, these were attributed to a change in the relative amplitude of the phases, with the fast:slow ratio being approximately 3:1 with bromoxynil and approximately 1:2 with DCMU at 300 K. Redox titrations of Q(A) were performed with and without herbicides at pH 6.5. The E(m) was shifted by approximately -75 mV by bromoxynil and by approximately +55 mV by DCMU. As the titrations were done over a time range that is assumed to be much longer than that for the transition between the two different populations, the potentials measured are considered to be a weighted average of two potentials for Q(A). The influence of the herbicides can thus be considered to be on the equilibrium of the two reaction center forms. This may also be the case in photosystem II.

Spectroscopic studies on electron transfer between plastocyanin and cytochrome b6f complex.

This paper reports the results of the research on the interaction between the highly active cytochrome b(6)f complex and plastocyanin, both isolated from the same source - spinachia oleracea plants. An equilibrium constant K between the cytochrome f of the cytochrome b(6)f complex and plastocyanin has been estimated by two independent spectroscopic techniques: steady-state absorption spectroscopy and stopped-flow. The second-order rate constants k2 for forward and backward electron transfer between cytochrome f and plastocyanin have been found between 1.4-2 x 10(7) and 8-10 x 10(6) M(-1)s(-1), respectively, giving the value of an equilibrium constant of about 2+/-0.4 or a difference in redox potential between plastocyanin and cytochrome f of cytochrome b(6)f complex of ca. 17 mV. The value of K=1.7+/-0.3 has been estimated from steady-state experiments in which the initial and final concentrations of participating components after mixing have been estimated via differential spectra analysis or spectra deconvolution. We propose a method of evaluation of the final plastocyanin concentration after the electron transfer reaction between cytochrome bf complex and plastocyanin that overcomes the interference by the strong chlorophyll absorption in the spectral region where oxidised plastocyanin has its low extinction absorption band. The data from both experiments, in the system devoid of quinol being the electron donor to cytochrome b(6), suggest that in case of electron transfer from cytochrome f to plastocyanin electron transfer can either bypass cytochrome f or the Rieske iron-sulfur protein can be reduced prior to its movement to the quinol binding site of cytochrome b(6). The role of the Rieske protein in forward and backward electron transfer reactions is discussed.

Inhibition of Photosystem II activity by saturating single turnover flashes in calcium-depleted and active Photosystem II.

Inhibition of Photosystem II (PS II) activity induced by continuous light or by saturating single turnover flashes was investigated in Ca(2+)-depleted, Mn-depleted and active PS II enriched membrane fragments. While Ca(2+)- and Mn-depleted PS II were more damaged under continuous illumination, active PS II was more susceptible to flash-induced photoinhibition. The extent of photoinactivation as a function of the duration of the dark interval between the saturating single turnover flashes was investigated. The active centres showed the most photodamage when the time interval between the flashes was long enough (32 s) to allow for charge recombination between the S(2) or S(3) and Q(B) (-) to occur. Illumination with groups of consecutive flashes (spacing between the flashes 0.1 s followed by 32 s dark interval) resulted in a binary oscillation of the loss of PS II-activity in active samples as has been shown previously (Keren N, Gong H, Ohad I (1995), J Biol Chem 270: 806-814). Ca(2+)- and Mn-depleted PS II did not show this effect. The data are explained by assuming that charge recombination in active PS II results in a back reaction that generates P(680) triplet and thence singlet oxygen, while in Ca(2+)- and Mn-depleted PS II charge recombination occurs through a different pathway, that does not involve triplet generation. This correlates with an up-shift of the midpoint potential of Q(A) in samples lacking Ca(2+) or Mn that, in term, is predicted to result in the triplet generating pathway becoming thermodynamically less favourable (G.N. Johnson, A.W. Rutherford, A. Krieger, 1995, Biochim. Biophys. Acta 1229, 201-207). The diminished susceptibility to flash-induced photoinhibition in Ca(2+)- and Mn-depleted PS II is attributed at least in part to this mechanism.

A large fraction of PsaF is nonfunctional in photosystem I complexes lacking the PsaJ subunit.

PsaJ is a small hydrophobic subunit of the photosystem I complex (PSI) whose function is not yet fully understood. Here we describe mutants of the green alga Chlamydomonas reinhardtii, in which the psaJ chloroplast gene has been inactivated either in a wild-type or in a PsaF-deficient nuclear background. Cells lacking one or both subunits grow photoautotrophically and contain normal levels of PSI. Flash-absorption spectroscopy performed with isolated PSI particles isolated from the PsaJ-deficient strain indicates that only 30% of the PSI complexes oxidize plastocyanin (Pc) or cytochrome c6 (Cyt c6) with kinetics identical to wild type, whereas the remaining 70% follow slow kinetics similar to those observed with PsaF-deficient PSI complexes. This feature is not due to partial loss of PsaF, as the PsaJ-less PSI complex contains normal levels of the PsaF subunit. The N-terminal domain of PsaF can be cross-linked to Pc and Cyt c6 indicating that in the absence of PsaJ, this domain is exposed in the lumenal space. Therefore, the decreased amount of functional PsaF revealed by the electron-transfer measurements is best explained by a displacement of the N-terminal domain of PsaF which is known to provide the docking site for Pc and Cyt c6. We propose that one function of PsaJ is to maintain PsaF in a proper orientation which allows fast electron transfer from soluble donor proteins to P700(+).

Insertion of the N-terminal part of PsaF from Chlamydomonas reinhardtii into photosystem I from Synechococcus elongatus enables efficient binding of algal plastocyanin and cytochrome c6.

A strain of the cyanobacterium Synechococcus elongatus was generated that expresses a hybrid version of the photosystem I subunit PsaF consisting of the first 83 amino acids of PsaF from the green alga Chlamydomonas reinhardtii fused to the C-terminal portion of PsaF from S. elongatus. The corresponding modified gene was introduced into the genome of the psaF-deletion strain FK2 by cointegration with an antibiotic resistance gene. The transformants express a new PsaF subunit similar in size to PsaF from C. reinhardtii that is assembled into photosystem I (PSI). Hybrid PSI complexes isolated from these strains show an increase by 2 or 3 orders of magnitude in the rate of P700(+) reduction by C. reinhardtii cytochrome c6 or plastocyanin in 30% of the complexes as compared with wild type cyanobacterial PSI. The corresponding optimum second-order rate constants (k2 = 4.0 and 1.7 x 10(7) M1 s1 for cytochrome c6 and plastocyanin) are similar to those of PSI from C. reinhardtii. The remaining complexes are reduced at a slow rate similar to that observed with wild type PSI from S. elongatus and the algal donors. At high concentrations of C. reinhardtii cytochrome c6, a fast first-order kinetic component (t(1)/(2) = 4 microseconds) is revealed, indicative of intramolecular electron transfer within a complex between the hybrid PSI and cytochrome c6. This first-order phase is characteristic for P700(+) reduction by cytochrome c6 or plastocyanin in algae and higher plants. However, a similar fast phase is not detected for plastocyanin. Cross-linking studies show that, in contrast to PSI from wild type S. elongatus, the chimeric PsaF of PSI from the transformed strain cross-links to cytochrome c6 or plastocyanin with a similar efficiency as PsaF from C. reinhardtii PSI. Our data indicate that development of a eukaryotic type of reaction mechanism for binding and electron transfer between PSI and its electron donors required structural changes in both PSI and cytochrome c6 or plastocyanin.

One-dimensional, nonlinear determinism characterizes heart rate pattern during paced respiration.

This study focuses on the dynamic pattern of heart rate variability in the frequency range of respiration, the so-called respiratory sinus arrhythmia. Forty experimental time series of heart rate data from four healthy adult volunteers undergoing a paced respiration protocol were used as an empirical basis. For pacing-cycle lengths >8 s, the heartbeat intervals are shown to obey a rule that can be expressed by a one-dimensional circle map (next-angle map). Circle maps are introduced as a new type of model for time series analyses to characterize the nonlinear dynamic pattern underlying the respiratory sinus arrhythmia during voluntary paced respiration. Although these maps are not chaotic, the dynamic pattern shows typical imprints of nonlinearity. By starting from a piecewise linear model, which describes the different circle maps obtained from the empirical time series for various pacing frequencies, time invariant measures can be introduced that characterize the dynamic pattern of heart rate variability during voluntary slow-paced respiration.

Effects of temperature and deltaGo on electron transfer from cytochrome c2 to the photosynthetic reaction center of the purple bacterium Rhodobacter sphaeroides.

The kinetics of electron transfer from cytochrome c2 to the primary donor (P) of the reaction center from the photosynthetic purple bacterium Rhodobacter sphaeroides have been investigated by time-resolved absorption spectroscopy. Rereduction of P+ induced by a laser pulse has been measured at temperatures from 300 K to 220 K in a series of specifically mutated reaction centers characterized by altered midpoint redox potentials of P+/P varying from 410 mV to 765 mV (as compared to 505 mV for wild type). Rate constants for first-order electron donation within preformed reaction center-cytochrome c2 complexes and for the bimolecular oxidation of free cytochrome c2 have been obtained by multiexponential deconvolution of the kinetics. At all temperatures the rate of the fastest intracomplex electron transfer increases by more than two orders of magnitude as the driving force -deltaGo is varied over a range of 350 meV. The temperature and deltaGo dependences of the rate constant fit the Marcus equation well. Global analysis yields a reorganization energy lambda = 0.96 +/- 0.07 eV and a set of electronic matrix elements, specific for each mutant, ranging from 1.2 10(-4) eV to 2.5 10(-4) eV. Analysis in terms of the Jortner equation indicates that the best fit is obtained in the classical limit and restricts the range of coupled vibrational modes to frequencies lower than approximately 200 cm(-1). An additional slower kinetic component of P+ reduction, attributed to electron transfer from cyt c2 docked in a nonoptimal configuration of the complex, displays a Marcus type dependence of the rate constant upon deltaGo, characterized by a similar value of lambda (0.8 +/- 0.1 eV) and by an average electronic matrix element smaller by more than one order of magnitude. In all of the mutants, as the temperature is decreased below 260 K, both intracomplex reactions are abruptly inhibited, their rate being negligible at 220 K. The free energy dependence of the second-order rate constant for oxidation of cyt c2 in solution suggests that the collisional reaction is partially diffusion controlled, reaching the diffusion limit at exothermicities between 150 and 250 meV over the temperature range investigated.

The N-terminal domain of PsaF: precise recognition site for binding and fast electron transfer from cytochrome c6 and plastocyanin to photosystem I of Chlamydomonas reinhardtii.

The PsaF-deficient mutant 3bF of Chlamydomonas reinhardtii was used to modify PsaF by nuclear transformation and site-directed mutagenesis. Four lysine residues in the N-terminal domain of PsaF, which have been postulated to form the positively charged face of a putative amphipathic alpha-helical structure were altered to K12P, K16Q, K23Q, and K30Q. The interactions between plastocyanin (pc) or cytochrome c6 (cyt c6) and photosystem I (PSI) isolated from wild type and the different mutants were analyzed using crosslinking techniques and flash absorption spectroscopy. The K23Q change drastically affected crosslinking of pc to PSI and electron transfer from pc and cyt c6 to PSI. The corresponding second order rate constants for binding of pc and cyt c6 were reduced by a factor of 13 and 7, respectively. Smaller effects were observed for mutations K16Q and K30Q, whereas in K12P the binding was not changed relative to wild type. None of the mutations affected the half-life of the microsecond electron transfer performed within the intermolecular complex between the donors and PSI. The fact that these single amino acid changes within the N-terminal domain of PsaF have different effects on the electron transfer rate constants and dissociation constants for both electron donors suggests the existence of a rather precise recognition site for pc and cyt c6 that leads to the stabilization of the final electron transfer complex through electrostatic interactions.

Membrane-anchored cytochrome cy mediated microsecond time range electron transfer from the cytochrome bc1 complex to the reaction center in Rhodobacter capsulatus.

In Rhodobacter capsulatus, the soluble cytochrome (cyt) c2 and membrane-associated cyt cy are the only electron carriers which operate between the photochemical reaction center (RC) and the cyt bc1 complex. In this work, cyt cy mediated microsecond time range electron transfer kinetics were studied by light-activated time-resolved absorption spectroscopy using a mutant strain lacking cyt c2. In intact cells and in isolated chromatophores of this mutant, only approximately 30% of the RCs had their photooxidized primary donor rapidly rereduced by cyt cy. Of these 30%, about half were reduced with a half-time of approximately 5 micros attributed to preformed complexes, and the other half with a half-time of approximately 40 micros attributed to cyt cy having to move from another site. This slower phase was affected by addition of glycerol, indicating its dependence on the viscosity of the medium. Cyt cy, despite its rereduction by ubihydroquinone oxidation in the millisecond time range, remained virtually unable to deliver electrons to other RCs which stayed photooxidized for several seconds. Furthermore, using two flashes separated by a variable time interval, it was shown that the fast electron donating complex was reformed in about 60 micros, a time span probably reflecting electron transfer from cyt c1 to cyt cy. In the absence of the cyt bc1 complex, the steady-state level of cyt cy in the chromatophore membranes obtained using cells grown in minimal medium was decreased to approximately 50%. The remaining cyt cy , however, was able to form the fast electron donating complex with the RC (half-time of approximately 5 micros), whereas the slower phase with a half-time of approximately 40 micros was strongly decelerated. This finding suggests a role for the cyt bc1 complex in stabilizing cyt cy and providing its "other" site, possibly via a close association between these components. Taken together, it is concluded that although cyt cy is present in substoichiometric amount compared to the RCs, it supports efficiently photosynthetic growth of R. capsulatus in the absence of cyt c2 because it can mediate fast electron transfer from the cyt bc1 complex to the RC during multiple turnovers of the cyclic electron flow.

Fast electron transfer from cytochrome c6 and plastocyanin to photosystem I of Chlamydomonas reinhardtii requires PsaF.

To study the function of the PsaF subunit of photosystem I (PSI), the interactions between plastocyanin or cytochrome c6 and PSI isolated from wild-type and a PsaF-deficient mutant of Chlamydomonas reinhardtii have been examined using cross-linking techniques and flash absorption spectroscopy. We show that efficient electron transfer from both plastocyanin and cytochrome c6 to PSI depends on PsaF. A remarkable feature of the PSI complex of C. reinhardtii is that both plastocyanin and cytochrome c6 reduce P700+ with first-order kinetics and a half-time of 3 micros, which is unique among photosynthetic organisms examined.

Cross-linked electron transfer complex between cytochrome c2 and the photosynthetic reaction center of Rhodobacter sphaeroides.

Electron donation from the soluble cytochrome (cyt) c2 to the photooxidized primary donor, P+, of reaction centers isolated from Rhodobacter sphaeroides was studied by using chemical zero-length cross-linking. This cross-linking stabilizes a 1:1 covalent complex between subunit M of the reaction center and cyt c2. In 80% of the reaction centers, P+ generated by a laser flash is reduced by covalently bound cyt c2. Kinetics of P+ reduction show (i) a fast phase with a half-life of 0.7 micros similar to that observed for electron transfer in the noncovalent proximal complex and (ii) a slow phase (t1/2 = 60 micros) that is attributed to a cyt c2 bound less favorably for electron transfer. Its relationship with similar kinetic phases attributed to a distal conformation of the complex in previous studies is discussed. Both kinetic phases are slightly accelerated upon addition of glycerol. Upon addition of reduced soluble cyt c2 to the cross-linked complex the kinetics of both phases are not affected. The kinetics of P+ reduction following the second flash (20 ms after the first) show that a complex is formed between soluble cyt c2 and the cross-linked complex, in which electron transfer takes place in the millisecond time domain. Cross-linked cyt c2 in complexes which give rise to the two kinetic phases of P+ reduction shows almost pH-independent midpoint redox potentials between pH 6 and 9.5. This behavior is at variance with that of free cyt c2, the midpoint potential of which is affected by at least two protonable groups within this pH range. The cross-linked RC-cyt c2 complex allowed study of the effects of temperature on the electron transfer reaction without a possible disturbance by dissociation of the complex. In the 250-300 K range, Arrhenius behavior is observed showing activation energies of 11.7 and 8.0 kJ/mol for the faster and the slower kinetic phases, respectively, which are remarkably lower than the activation energy of 20.5 kJ/mol for the fast P+ reduction by soluble cyt c2 [Venturoli, G., Mallardi, A., & Mathis, P. (1993) Biochemistry 32, 13245-13253]. Between 250 and 230 K, a fall-off in amplitude is observed for both kinetic phases indicating that intracomplex electron transfer is blocked at low temperatures.

Structure and function of cytochrome c2 in electron transfer complexes with the photosynthetic reaction center of Rhodobacter sphaeroides: optical linear dichroism and EPR.

The photosynthetic reaction center (RC) and its secondary electron donor the water-soluble cytochrome (cyt) c2 from the purple bacterium Rhodobacter sphaeroides have been used in cross-linked and non-cross-linked complexes, oriented in compressed gels or partially dried multilayers, to study the respective orientation of the primary donor P (BChl dimer) and of cyt c2. Three methods were used: (i) Polarized optical absorption spectra at 295 and 10 K were measured and the linear dichroism of the two individual transitions (Qx, Qy), which are nearly degenerate within the alpha-band of reduced cyt c2, was determined. Attribution of the polarization directions to the molecular axes within the heme plane yielded the average cyt orientation in the complexes. (ii) Time-resolved flash absorption measurements using polarized light allowed determination of the orientation of cyt c2 in complexes which differ in their kinetics of electron transfer. (iii) EPR spectroscopy of ferricyt c2 in cross-linked RC-cyt c2 complexes was used to determine the angle between the heme and the membrane plane. The results suggest the following structural properties for the docking of cyt c2 to the RC: (i) In cross-linked complexes, the two cytochromes displaying half-lives of 0.7 and 60 micros for electron transfer to P+ are similarly oriented (difference < 10 degrees). (ii) For cross-linked cyt c2 the heme plane is parallel to the symmetry axis of the RC (0 degrees +/- 10 degrees). Moreover, the Qy transition, which is assumed to be polarized within the ring III-ring I direction of the heme plane, makes an angle of 56 degrees +/- 1 degree with the symmetry axis. (iii) The dichroism spectrum for the fast phase (0.7 micros) for the non-cross-linked cyt c2-RC complex suggests an orientation similar to that of cross-linked cyt c2, but the heme plane is tilted about 20 degrees closer to the membrane. An alternative model is that two or more bound states of cyt c2 with heme plane tilt angles between 0 degrees and 30 degrees allow the fast electron transfer. Zero-length cross-linking of cyt c2 may take place in one of these bound states. These orientations of cyt c2 are compared to different structural models of RC-cyt c2 complexes proposed previously. The relation of the two kinetic phases observed in cross-linked cyt c2 complexes to biphasic kinetics of the mobile reaction partners is discussed with respect to the dynamic electrostatic interactions during the formation of a docking complex and its dissociation. A mechanism is proposed in which a pre-orientation of cyt c2 relative to the membrane plane occurs by interaction of its strong electrostatic dipole with the negative surface charges of the RC. The optimal matching of the oppositely charged surfaces of the two proteins necessitates further rotation of the cyt around its dipole axis.

Hydrogen-bond interactions of the primary donor of the photosynthetic purple sulfur bacterium Chromatium tepidum.

We have used near-infrared Fourier transform (pre)resonance Raman spectroscopy to determine the protein interactions with the bacteriochlorophyll (BChl) dimer constituting the primary electron donor, P, in the reaction center (RC) from the thermophilic purple sulfur bacterium Chromatium tepidum. In addition, we report the alignment of partial sequences of the L and M protein subunits of C. tepidum RCs in the vicinity of the primary donor with those of Rhodobacter sphaeroides and Rhodopseudomonas viridis. Taken together, these results enable us to propose the hydrogen-bonding pattern and the H-bond donors to the conjugated carbonyl groups of P. Selective excitation (1064-nm laser radiation) of the FT (pre)-resonance Raman spectra of P in its neutral (P degree) and oxidized (P degree +) states were obtained via their electronic absorption bands at 876 and 1240 nm, respectively. The P degree spectrum exhibits vibrational frequencies at 1608, 1616, 1633, and 1697 cm-1 which bleach upon P oxidation. The P degree + spectrum exhibits new bands at 1600, 1639, and 1719 cm-1. The 1608-cm-1 band, which downshifts to 1600 cm-1 upon oxidation, is assigned to a CaCm methine bridge stretching mode of the P dimer, indicating that each BChl molecule possesses a single axial ligand (His L181 and His M201, from the sequence alignment). The 1616- and 1633-cm-1 bands correspond to two H-bonded pi-conjugated acetyl carbonyl groups of each BChl molecule. with different H-bond strengths: the 1616-cm-1 band is assigned to the PL C2 acetyl group which is H-bonded to a histidine residue (His L176), while the 1633-cm-1 band is assigned to the PM C2 acetyl carbonyl, H-bonded to a tyrosine residue (Tyr M196). Both PL and PM C9 keto carbonyls are free from interactions and vibrate at the same frequency (1697 cm-1). Thus, the H-bond pattern of the primary donor of C. tepidum differs from that of Rb. sphaeroides in the extra H-bond to the PM C2 acetyl carbonyl group; that of PL is H-bonded to a histidine residue in both primary donors (His L168 in Rb. sphaeroides and His L176 in C. tepidum). The P degree/P degree + redox midpoint potentials were measured to be +497 and +526 mV for isolated C. tepidum RCs with and without the associated tetraheme cytochrome c subunit, respectively, and +502 mV for intracytoplasmic membranes. The positive charge localization was estimated to be 69% in favor of PL, indicating a more delocalized situation over the primary donor of C. tepidum than that of Rb. sphaeroides (estimated to be 80% on PL). These differences in physicochemical properties are discussed with respect to the proposed structural model for the microenvironment of the primary donor of C. tepidum.

Binding dynamics and electron transfer between plastocyanin and photosystem I.

The mechanism of the electron transfer from the soluble protein plastocyanin to the multiprotein complex of photosystem I from spinach has been studied in detail. The two kinetic components of P700+ reduction by plastocyanin after a laser flash, showing a constant half-life of 11 microseconds and a variable half-life of the second-order reaction, respectively, are used to monitor the electron transfer from bound and soluble plastocyanin. The effect of increasing concentration of reduced plastocyanin on both of these kinetic components and the competition by oxidized plastocyanin is used to estimate the individual dissociation constants of the complex between the proteins in each of its oxidized and reduced state. The dissociation constant of oxidized plastocyanin is about six times larger than that of 7 microM found for reduced plastocyanin and purified PSI. Consistent with this result the midpoint redox potential of plastocyanin bound to photosystem I either in equilibrium with soluble plastocyanin or after cross-linking to photosystem I is found to be 50-60 mV higher than that of soluble plastocyanin. It is concluded that the driving force of the intracomplex electron transfer is decreased in favor of an optimized turnover of photosystem I. Double-flash excitation shows that oxidized plastocyanin has to leave the complex after the electron transfer before a new reduced plastocyanin molecule can bind to photosystem I. This release of oxidized plastocyanin with a half-life of about 60 microseconds limits the turnover of photosystem I. All data are consistently described by a model including the formation of a complex at a single binding site of photosystem I. Differences in the rate and binding constants are discussed with respect to the structure and the electrostatic and hydrophobic interactions stabilizing the complex as well as their modification by the membrane environment in situ.

[Methodology in the analysis of asymmetry in fluctuations of heart rate]. / Methodik der Analyse der Asymmetrie in den Fluktuationen der Herzfrequenz.

Time series of R-R intervals show fluctuations which are neither symmetric regarding the changes in length of heart beats nor regarding the number of heart beats during the phases of heart rate acceleration and deceleration. These features of heart rate variability cannot be quantified by the analysis of the beat-to-beat variability or by the spectrum analysis of heart rate. The analysis of asymmetry using the distribution function of the differences between consecutive R-R intervals creates measures for the total, central, and peripheral asymmetry. These measures quantify different aspects of the shape of the distribution function. The asymmetry measures are either based on the amount of difference between consecutive R-R intervals or the number of lengthening R-R intervals in a sequence of heart beats. The analysis of asymmetry of R-R interval time series shows differences among test subjects during rest.

[Mathematical model of "respiratory sinus arrhythmia"]. / Mathematisches Modell der "respiratorischen Sinusarrhythmie".

We developed a mathematical model of "respiratory" sinus arrhythmia. The model combines a representation continuous in time of the parasympathetic and sympathetic innervation and the membrane potential of the pace maker cell of the heart with a beat-by-beat representation of the cardiovascular variables like diastolic and systolic blood pressure, pulse pressure, total peripheral resistance and baroreceptor activity. The influence of respiration is described separately by mechanical and central neural mechanisms. Using this nonlinear model of "respiratory" heart rate variability one is able to explore in a theoretical way the different heart rate variability generating mechanisms, either as isolated or combined effects on both, heart rate variability in the frequency range of respiration and in the frequency range around 0.1 Hz. By fitting a simulated RR interval time course to a physiological RR interval time course one can estimate the relative weight of the different mechanisms generating this physiological heart rate variability.

Lateral diffusion of an integral membrane protein: Monte Carlo analysis of the migration of phosphorylated light-harvesting complex II in the thylakoid membrane.

The lateral migration of the integral light-harvesting chlorophyll a/b protein complex of photosystem II, LHCII, has been studied in the undisturbed membranes of thylakoids without artificial probes. LHCII was phosphorylated at 0 degree C. The diffusion of the mobile phospho-LHCII from appressed grana to nonappressed membrane regions was induced by a temperature jump to 20 degrees C and analyzed by a rapid detergent fractionation of the two membrane areas. This long-range diffusion of the integral phospho-LHCII is analyzed by a Monte Carlo calculation which is based on a model of the thylakoid membrane and includes all integral proteins as mobile particles. A comparison of the calculation with the experimental time course indicates a diffusion constant of phospho-LHCII in the range of (2-4) x 10(-12) cm2 s-1. This value is evidence for a severe restriction of protein mobility in the appressed thylakoid membrane. From a statical point of view, the percolation theory predicts that the high protein density in the grana membranes is above the threshold of percolation and the long-range diffusion should be inhibited by finite clusters of lipids. However, the shape of the experimental time course is in favor of a lateral motion also of photosystem II and nonphosphorylated LHCII and not of a rigid lattice of these complexes. Our data and Monte Carlo analysis suggest a dynamic or fluid lattice of the protein complexes with a lifetime of the clusters in the millisecond time range. The consequences of these transient fluctuations on the long-range diffusion of plastoquinone are discussed.