Evolution of dissipative system: a theoretical basis of Margalef's principle on ecosystem

The concepts of fitness and survival in logistic models are shown to be independent if we follow certain intuitive definitions for these concepts. This conclusion follows from a simple topological analysis of the function f_b (x) = bx (1?x), which is just the standard form of the logistic growth equations.     

The effects of detergents DDM and β-OG on the singlet excited state lifetime of the chlorophyll a in cytochrome b6f complex from spinach chloroplasts

The singlet excited state lifetime of the chlorophyll a (Chi a) in cytochrome b6f (Cyt b6f) complex was reported to be shorter than that of free Chl a in methanol, but the value was different for Cyt b6f complexes from different sources (～200 and ～600 ps are the two measured results). The present study demonstrated that the singiet excited state lifetime is associated with the detergents n-dodecyl-β-D-maltoside (DDM) and n-octyl-β-D-glucopyranoside (β-OG), but has nothing to do with the different sources of Cyt b6f complexes. Compared with the Cyt b6f dissolved in β-OG, the Cyt b6f in DDM had a lower fluorescence yield, a lower photodegradation rate of Chl a, and a shorter lifetime of Chl a excited state. In short, the singlet excited state lifetime, ～200 ps, of the Chl a in Cyt b6f complex in DDM is closer to the true in vivo.     

The effects of detergents DDM and β-OG on the singlet excited state lifetime of the chlorophyll a in cytochrome b6f complex from spinach chloroplasts

The singlet excited state lifetime of the chlorophyll a (Chl a) in cytochrome b ₆ f (Cyt b ₆ f) complex was reported to be shorter than that of free Chl a in methanol, but the value was different for Cyt b ₆ f complexes from different sources (∼200 and ∼600 ps are the two measured results). The present study demonstrated that the singlet excited state lifetime is associated with the detergents n-dodecyl-β-D-maltoside (DDM) and n-octyl-β-D-glucopyranoside (β-OG), but has nothing to do with the different sources of Cyt b ₆ f complexes. Compared with the Cyt b ₆ f dissolved in β-OG, the Cyt b ₆ f in DDM had a lower fluorescence yield, a lower photodegradation rate of Chl a, and a shorter lifetime of Chl a excited state. In short, the singlet excited state lifetime, ∼200 ps, of the Chl a in Cyt b ₆ f complex in DDM is closer to the true in vivo.     

On the mode of integration of plastid-encoded components of the cytochrome bf complex into thylakoid membranes

Four distinct integration/translocation routes into/across thylakoid membranes have recently been deduced for nuclear-encoded polypeptides of the photosynthetic membrane. Corresponding information for the plastid-encoded protein complement is lacking. We have investigated this aspect with in-organello assays employing chimeric constructs generated with codon-correct cassettes for genes of plastid-encoded thylakoid proteins, and appropriate transit peptides from six nuclear genes, representing three targeting classes, as a strategy. The three major plastid-encoded components of the cytochrome b ₆  f complex, namely pre-apocytochrome f, (including apocytochrome f, and pre-apocytochrome f lacking the C-terminal transmembrane segment), cytochrome b ₆ , and subunit IV, which differ in the number of their transmembrane segments, were studied. Import into chloroplasts could be observed in all instances but with relatively low efficiency. Thylakoid integration can occurr post-translationally, but only components with secretory/secretory pathway (SEC)-route-specific epitopes were correctly assembled with the cytochrome complex, or competed with this process. Inhibitor studies were consistent with these findings. Imported cytochrome b ₆ and subunit IV operated with uncleaved targeting signals for thylakoid integration. The corresponding determinant for cytochrome f is its signal peptide; its C-terminal hydrophobic segment did not, or did not appreciably, contribute to this process. The N-termini of cytochrome b ₆ and subunit IV appear to reside on the same (lumenal) side of the membrane, consistent with the currently favored four-helix model for the cytochrome, but in disagreement with the topography proposed for both components. The impact of the findings for protein routing, including for applied approaches such as compartment-alien transformation, is discussed. Received: 18 September 1996 / Accepted: 15 October 1996     

High-light-induced superoxide anion radical formation in cytochrome <Emphasis Type="Italic">b</Emphasis><Subscript><Emphasis Type="Italic">6</Emphasis></Subscript><Emphasis Type="Italic">f</Emphasis> complex from spinach as detected by EPR spectroscopy

The generation of superoxide anion radical (O₂ ^·−) in the cytochrome b ₆ f complex (Cyt b ₆ f) of spinach under high-light illumination was studied using electron paramagnetic resonance spectroscopy. The generation of O₂ ^·− was lost in the absence of molecular oxygen. It was also suppressed in the presence of NaN₃ and could be scavenged by extraneous antioxidants such as ascorbate, β-carotene, and glutathione. The results also indicate that O₂ ^·−, which is produced under high-light illumination of the Cyt b ₆ f from spinach, might be generated from a reaction involing ¹O₂, and the Rieske Fe-S protein could serve as the electron donor in the O₂ ^·− production. The mechanism of photoprotection of the Cyt b ₆ f complex by antioxidants is discussed.     

Kinetic studies of electron transfer in the cyt b 5 : metHb system

 The kinetics of methemoglobin reduction by cytochrome b ₅ has been studied by stopped-flow and saturation transfer NMR. A forward rate constant k _f = 2.44×10⁴ M^–1 s^–1 and a reverse rate constant k _b = 540 M^–1s^–1 have been observed at 10 mm, pH 6.20, 25  °C. The ratio k _f/k _b = k _eq = 43.6 is in good agreement with the equilibrium constant calculated from the electrochemical potential between cyt b ₅ and methemoglobin. A bimolecular collisional mechanism is proposed for the electron transfer from cyt b ₅ to methemoglobin based on the kinetic data analysis. The dependence of the rate constants on ionic strengths supports such collisional mechanism. It is also found that the reaction rate strongly depends on the conformations of methemoglobin. Received: 20 February 1996 / Accepted: 4 June 1996     

The qualitative analysis of a difference equation of population growth

The difference equation f _b :[0,1]–[0,1] defined by f _b (x)=b x(1–x) is studied. In particular complete qualitative information is obtained for the parameter value b=3.83. For example the number of fixed points of (f _b )ⁱ is given by

Galerkin-Ritz procedures for approximate solutions to systems of reaction-diffusion equations

For any essentially nonlinear system of reaction-diffusion equations of the generic form ∂c_i/∂t=D_i∇²c_i+Q_i(c,x,t) supplemented with Robin type boundary conditions over the surface of a closed bounded three-dimensional region, it is demonstrated that all solutions for the concentration distributionn-tuple function c=(c ₁(x,t),...,c _n (x,t)) satisfy a differential variational condition. Approximate solutions to the reaction-diffusion intial-value boundary-value problem are obtainable by employing this variational condition in conjunction with a Galerkin-Ritz procedure. It is shown that the dynamical evolution from a prescribed initial concentrationn-tuple function to a final steady-state solution can be determined to desired accuracy by such an approximation method. The variational condition also admits a systematic Galerkin-Ritz procedure for obtaining approximate solutions to the multi-equation elliptic boundary-value problem for steady-state distributions c=−c(x). Other systems of phenomenological (non-Lagrangian) field equations can be treated by Galerkin-Ritz procedures based on analogues of the differential variational condition presented here. The method is applied to derive approximate nonconstant steady-state solutions for ann-species symbiosis model.     

Singlet oxygen formation and chlorophyll a triplet excited state deactivation in the cytochrome b6f complex from Bryopsis?corticulans

We have attempted to investigate the correlation between the detergent-perturbed structural integrity of the Cyt b ₆ f complex from the marine green alga Bryopsis corticulans and its photo-protective properties, for which the nonionic detergents n-octyl-β-d-glucopyranoside (β-OG) and n-dodecyl-β-d-maltoside (β-DM), respectively, were used for the preparation of Cyt b ₆ f, and the singlet oxygen (¹O₂*) production as well as the triplet excited-state chlorophyll a (³Chl a*) formation and deactivation were examined by spectroscopic means. Near-infrared luminescence of ¹O₂ * (~1,270 nm) on photo-irradiation was detected for the β-OG preparation where the complex is mainly in oligomeric state, but not for the β-DM one in which the complex exists in dimeric form. Under anaerobic condition, photo-excitation of Chl a in the β-DM preparation generated ³Chl a* with a lower quantum yield of Φ_T ~ 0.02 and a longer lifetime of ~600 μs with respect to those as in the case of β-OG preparation, Φ_T ~ 0.12 and 200–300 μs. These results prove that the enzymatically active and intact Cyt b ₆ f complex on photo-excitation tends to produce little ³Chl a* or ¹O₂ *, which implies that the pigment–protein assembly of Cyt b ₆ f complex per se is crucial for photo-protection. F. Ma and X.-B. Chen contributed equally to this work.     

Bounds on the total particle number for species governed by reaction-diffusion equations in the infinite spatial domain

Differential inequality methods are developed for establishing upper and lower bounds on the total particle numberN(t)=∫θ(x,t) d³ x associated with solutions to nonlinear reaction-diffusion equations of the form ∂θ/∂t=D∇²θ+fθ-gθ ⁿ⁺¹ , whereD(>0),n(>0),f andg are constant parameters. If finite in a neighborhood oft=0,N(t) is bounded below for allt≥0 by a certain derived function oft for equations withg≥0. An upper bound onN(t) is obtained for equations withn=1,f<0 andg<0. These results provide general preservation and extinction criteria for the total particle number.     

Involvement of plastoquinone and lipids in electron transport reactions mediated by the cytochrome b6-f complex isolated from spinach

The isolation of a cytochrome b₆-f complex from spinach, which is depleted of plastoquinone (and lipid), is reported. The depleted complex no longer functions as a plastoquinol-plastocyanin oxidoreductase but can be reconstituted with plastoquinone and exogenous lipids. The lipid classes digalactosyldiacylglycerol, phosphatidylglycerol and phosphatidylcholine were active in reconstitution while monogalactosyldiacylglycerol and sulfoquinovosyldiacylglycerol were not. Neither plastoquinone nor lipid alone fully reconstitutes electron transport in the depleted complex. Saturation of plastoquinol-plastocyanin oxidoreductase activity in the depleted complex occurs at 1 plastoquinone per cytochrome f.     

The peroxidase activity of cytochrome <Emphasis Type="Italic">b</Emphasis><Subscript>6</Subscript><Emphasis Type="Italic">f</Emphasis> complex from spinach chloroplasts

The cytochrome b ₆ f (Cyt b ₆ f) complex, which functions as a plastoquinol-plastocyanin oxidoreductase and mediates the linear electron flow between photosystem II (PSII) and photosystem I (PSI) and the cyclic electron flow around PSI, was isolated from spinach (Spinacia oleracea L.) chloroplasts using n-octyl-β-D-glucopyranoside (β-OG). The preparation was also able to catalyze the peroxidase-like reaction in the presence of hydrogen peroxide (H₂O₂) and guaiacol. The optimal conditions for peroxidase activity of the preparation included: pH 3.6, ionic strength 0.1, and temperature 35°C. The apparent Michaelis constant (K _m) values for H₂O₂ and guaiacol were 50 mM and 2 mM, respectively. The bimolecular rate constant (k _obs) was about 26 M⁻¹ s⁻¹ and the turnover number (K _cat) was about 60 min⁻¹ (20 mM guaiacol, 100 mM sodium phosphate, pH 3.6, 25°C, [H₂O₂]<100mM). These parameters were similar to those of several other heme-containing proteins, such as myoglobin and Cyt c.     

Cytochrome b 6 f complex: Dynamic molecular organization,function and acclimation

The cytochrome b ₆ f complex occupies a central position in photosynthetic electron transport and proton translocation by linking PS II to PS I in linear electron flow from water to NADP⁺, and around PS I for cyclic electron flow. Cytochrome b ₆ f complexes are uniquely located in three membrane domains: the appressed granal membranes, the non-appressed stroma thylakoids and end grana membranes, and also the non-appressed grana margins, in contrast to the marked lateral heterogeneity of the localization of all other thylakoid multiprotein complexes. In addition to its vital role in vectorial electron transfer and proton translocation across the membrane, cytochrome b ₆ f complex is also involved in the regulation of balanced light excitation energy distribution between the photosystems, since its redox state governs the activation of LHC II kinase (the kinase that phosphorylates the mobile peripheral fraction of the chlorophyll a/b-proteins of LHC II of PS II). Hence, cytochrome b ₆ f complex is the molecular link in the interactive co-regulation of light-harvesting and electron transfer.The importance of a highly dynamic, yet flexible organization of the thylakoid membranes of plants and green algae has been highlighted by the exciting discovery that a lateral reorganization of some cytochrome b ₆ f complexes occurs in the state transition mechanism both in vivo and in vitro (Vallon et al. 1991). The lateral redistribution of phosphorylated LHC II from stacked granal membrane regions is accompanied by a concomitant movement of some cytochrome b ₆ f complexes from the granal membranes out to the PS I-containing stroma thylakoids. Thus, the dynamic movement of cytochrome b ₆ f complex as a multiprotein complex is a molecular mechanism for short-term adaptation to changing light conditions. With the concept of different membrane domains for linear and cyclic electron flow gaining credence, it is thought that linear electron flow occurs in the granal compartments and cyclic electron flow is localised in the stroma thylakoids at non-limiting irradiances. It is postulated that dynamic lateral reversible redistribution of some cytochrome b ₆ f complexes are part of the molecular mechanism involved in the regulation of linear electron transfer (ATP and NADPH) and cyclic electron flow (ATP only). Finally, the molecular significance of the marked regulation of cytochrome b ₆ f complexes for long-term regulation and optimization of photosynthetic function under varying environmental conditions, particularly light acclimation, is discussed.Abbreviations Chl chlorophyll - cyt cytochrome - PS Photosystem     

Relationship between oxygen saturation of mixed venous blood and pressure in the pulmonary artery trunk in healthy humans and patients with heart defects

The relationship between pulmonary artery pressure (P _LA) and oxygen saturation of mixed venous blood (S _V ) has been studied in subjects (1750 men and 1026 women) subdivided into 12 groups. Functional relationships have been found between P _LA and S _V , P _LA = f(S _V ), and S _V = f(P _LA), which were estimated using direct measurement of P _LA and S _V for each group. These factors have been found to obey the following dependences: P _LA = f(S _V ) and P _LA = a(S _V )^−b , where b = −0.2284a + 0.6564 in men and b = −0.285a + 1.2947 in women; S _V = f(P _LA) and S _V = c(P _LA)^−d , where d = −0.25131Ln(c) + 1.0212; R ² = 0.8993 in men and d = −1.9645Ln(c) + 2.852; and R ² = 0.9674 in women. Each group occupies a position on the curves specified by the equations. Subjects with the diagnosis of a functional heart murmur and patients with congenital aortic valve stenosis were grouped together to form the so-called normal group characterized by specific P _LA = f(S _V ) and S _V = f(P _LA) dependences. Male patients with coronary heart disease were also included in the normal group. An equation was derived to relate P _LA caused by different reasons with the corresponding saturation of mixed venous blood. In the case of the changing saturation of mixed venous blood, this equation gives the corresponding value of P _LA. Equilibrium between systemic and pulmonary circulations is established through interdependent changes in the physiological indices of blood circulation and gas exchange in humans.     

Mathematical biosociology of beliefs and prejudices

Following a suggestion made previously (Bull. Math. Biophysics,13, 61, 1951), it is assumed that every individual has both a tendency to behavearationally, by accepting everything on faith, and rationally, by subjecting everything to rational analysis. Arational behavior is characterized by various beliefs, prejudices, etc., which are considered to be conditioned reactions, learned by the individual before he completely develops his faculties for rational thinking. The two tendencies are assumed to be due to excitations of two different regions of the central nervous system, and are measured by the intensities ɛ _f and ɛ _r of those excitations. Those intensities are further assumed to increase linearly with time, the increases of the two beginning, in general, at different ages. The rates of increase are considered as normally distributed in the population. The relative frequency of arational and rational behavior is determined by the difference φ=ɛ _f =ɛ _r according to equations 0 developed previously (Bull. Math. Biophysics,11, 255, 1949). It is shown that with the above assumptions the majority of the population, which starts with arational behavior, will, within two or three of generations, either change to rational behavior or continue indefinitely to behave arationally. This will hold as long as imitative factors are present. Expressions for the numbers of individuals who behave rationally and arationally are derived. If the intensity of conditioning toward an arational behavior decreases with increasing size of the rationally behaving minority, or, if the rationally behaving individuals are not influenced by imitation, then a slow secular trend toward rational behavior may be present. An expression is also derived for the fraction of individuals who behave rationally as a function of age. This fraction increases with increase of the age at which the beginning conditioning toward any beliefs or prejudices begins.     

Some remarks on the Kedem-Katchalsky equations for non-electrolytes

The Kedem-Katchalsky equation for the flow of a non-electrolyte through a homogeneous membrane is shown to be a first order expansion of an exact integral of the Spiegler-Bearman-Kirkwood frictional equations under the assumption that the partial frictional coefficients, ζ _ij , are concentration independent. The equations are solved in terms of volume flow; there are no water-to-volume flow correction terms for the permeability, ω, or the reflection coefficient, σ. The precision of the expansion depends upon the magnitude of the water flow. The frictional coefficientsf _sm andf _sw are given as functions of the experimentally determined parameters ω and σ; the frictions, are shown to be independent ofL _p .     

Interaction between cadmium, zinc and silver-substituted plastocyanin and cytochrome b 6 f complex — heavy metals toxicity towards photosynthetic apparatus

This paper reports the results of research on the interaction between the cytochrome f of the active cytochrome b ₆ f complex (incubated with Cd-, Zn-, and Ag-substituted plastocyanins) and Cu-plastocyanin. The presented studies show, that the metal derivatives of plastocyanin can have an influence on the photosynthetic electron transfer path: cytochrome b ₆ f complex — photosystem I. The metal-substituted plastocyanins occupy the plastocyanin electron transfer site of the cytochrome f. The stopped-flow measurements show, that although the metal derivatives of plastocyanin do not influence the rate of cyt f- Pc electron transfer, creation of the non-electron-transfer complexes characterised by a strong binding between the cyt f and substituted plastocyanins and their slow release, dependent on the redox state of the substituted metal, results in the decrease of a turnover of the cytochrome complex. The research was done in the Department of Plant Biochemistry, Freiburg University, Sch?nzlestrasse 1, 79 104 Freiburg, Germany     

Chlorophyll a is the crucial redox sensor and transmembrane signal transmitter in the cytochrome b6f complex. Components and mechanisms of state transitions from the hydrophobic mismatch viewpoint

The cytochrome (cyt) b₆f complex is involved in the transmembrane redox signaling that triggers state transitions in cyanobacteria and chloroplasts. However, the components and molecular mechanisms are still unclear. In an attempt to solve this long-standing problem, we first focused on the unknown role of a single chlorophyll a (Chla) in cyt b₆f with a new approach based on Chla structural properties. Various b₆f X-ray crystal structures were analyzed to identify their differences, which correlate with differences in Chla molecular volume. We found that the distance of the Rieske [2Fe-2S] cluster to Chla correlates with the distance between a pair of residues at the Q_o-site and the distance between a pair of residues at the opposite membrane side. These correlations were accompanied by the rotation of a key peripheral residue and by changes in the hydrophobic thickness of cyt b₆f. Parallel analysis of cyt bc₁ crystal structures allowed us to conclude that Chla acts as the crucial redox sensor and transmembrane signal transmitter in b₆f for changes in the plastoquinone pool redox state. The hydrophobic mismatch induced by the changed hydrophobic thickness of cyt b₆f is the driving force for the structural reorganizations of the photosynthetic apparatus during induction and the progression of state transitions in cyanobacteria and chloroplasts. A mechanism for LHCII kinase activation in chloroplasts is also proposed. Our understanding of the dynamic structural changes in bc-complexes during turnover at the Q_o-site and state transitions is augmented by the time-sequence ordering of 56 bc crystal structures.     

Effect of cold exposure (?15°C) and Salbutamol treatment on physical performance in elite nonasthmatic cross-country skiers

The effects of whole-body exposure to ambient temperatures of −15°C and 23°C on selected performance-related physiological variables were investigated in elite nonasthmatic cross-country skiers. At an ambient temperature of −15°C we also studied the effects of the selective β₂-adrenergic agonist Salbutamol (0.4 mg × 3) which was administered 10 min before the exercise test. Eight male cross-country skiers with known maximal oxygen uptakes (V˙O_{2 max} ) of more than 70 ml · kg⁻¹ · min⁻¹ participated in the study. Oxygen uptake (V˙O₂), heart rate (f _c), blood lactate concentration ([La⁻]_b) and time to exhaustion were measured during controlled submaximal and maximal running on a treadmill in a climatic chamber. Lung function measured as forced expiratory volume in 1 s (FEV₁) was recorded immediately before the warm-up period and at the conclusion of the exercise protocol. Submaximal V˙O₂ and [La⁻]_b at the two highest submaximal exercise intensities were significantly higher at −15°C than at 23°C. Time to exhaustion was significantly shorter in the cold environment. However, no differences in V˙O_{2 max} or f _c were observed. Our results would suggest that exercise stress is higher at submaximal exercise intensities in a cold environment and support the contention that aerobic capacity is not altered by cold exposure. Furthermore, we found that after Salbutamol inhalation FEV₁ was significantly higher than after placebo administration. However, the inhaled β₂-agonist Salbutamol did not influence submaximal and maximal V˙O₂, f _c, [La⁻]_b or time to exhaustion in the elite, nonasthmatic cross-country skiers we studied. Thus, these results did not demonstrate any ergogenic effect of the β₂-agonist used. Accepted: 18 August 1997