Tight bounds on the convergence rate of generalized ratio consensus algorithms

The problems discussed in this paper are motivated by general ratio consensus algorithms, introduced by Kempe, Dobra, and Gehrke (2003) in a simple form as the push-sum algorithm, later extended by B\'en\'ezit et al. (2010) under the name weighted gossip algorithm. We consider a communication protocol described by a strictly stationary, ergodic, sequentially primitive sequence of non-negative matrices, applied iteratively to a pair of fixed initial vectors, the components of which are called values and weights defined at the nodes of a network. The subject of ratio consensus problems is to study the asymptotic properties of ratios of values and weights at each node, expecting convergence to the same limit for all nodes. The main results of the paper provide upper bounds for the rate of the almost sure exponential convergence in terms of the spectral gap associated with the given sequence of random matrices. It will be shown that these upper bounds are sharp. Our results complement previous results of Picci and Taylor (2013) and Iutzeler, Ciblat and Hachem (2013)

Kinetic limitations in turnover of photosynthetic bacterial reaction center protein

The membrane-bound reaction center from purple nonsulfur photosynthetic bacterium Rhodobacter sphaeroides performs light-induced charge separation and exports two molecules of oxidized cytochrome and one molecule of fully reduced quinone (quinol) from two opposite (periplasmic and cytoplasmic) sites of the protein during a single turnover. The rate of the turnover was measured based on cytochrome photooxidation under intense and continuous illumination of a laser diode that mimicks the open field conditions for photosynthetic organisms. At the highest intensity of illumination, the primary photochemistry was driven by a rate constant of 4,800 s-1. Factors limiting the steady-state turnover rate of the reaction center were studied under wide variety of conditions of light intensity, ionic strength, heavy metal ion binding and pH. The reaction center was solubilized in detergent, and reduced mammalian cytochrome c and oxidized ubiquinone were the exogenous electron donor and acceptor to the reaction center, respectively. Depending on the conditions, the kinetic limitation was attributed to light intensity, or to donor and acceptor side reactions. At low light intensities (<1,000 s -1, in terms of initial rate of photochemistry), the turnover rate was limited only by the light intensity. At higher intensities, however, the unbinding of the oxidized cytochrome at the donor side (acidic and neutral pH range) or the proton coupled interquinone electron transfer (alkaline pH range) were the bottlenecks of the turnover of the reaction center. The possible entries and pathways of protons to the secondary quinone are discussed based on multiple turnover of the reaction center

Competitive binding of quinone and antibiotic stigmatellin to reaction centers of photosynthetic bacteria

Stigmatellin bound to the QB site of the reaction center of photosynthetic bacteria is one of the most potent inhibitors of interquinone electron transfer. In addition to its inhibitory effect, it can be used to model protonated semiquinone and to probe the electrostatic environment. These properties were studied by two independent methods in isolated reaction centers and in chromatophores from cytochrome c-less mutant of Rhodobacter sphaeroides. The binding of the stigmatellin was detected by photochemical assay (flash-induced charge recombination of the reaction center) and the protonation/deprotonation equilibrium of the phenolic group by spectral assay monitoring the band peaks at 272 nm and 340 nm of the absorption spectra of the stigmatellin (Δe272(deprot/prot) = 10 mM-1·cm-1). The dissociation constant of stigmatellin binding increased by about two orders of magnitude from 4 nM (pH 8.5) to 350 nM (pH 11.0) in chromatophores indicating the difference in binding affinities between the protonated and deprotonated forms of the stigmatellin. The observed pK of the phenolic proton has proved to be very sensitive to the surroundings: 9.4 (in aqueous solution), 9.4-10.3 (in different detergents) and 10.2 (in excess to RC in detergent n-octyl-b-D-glycopyranoside). This wide range of values may indicate highly different electric fields (energetic coupling with the phenolic proton of the stigmatellin) and/or solvation energy of stigmatellin in different phases of the detergent/protein/membrane system

Fluorescence induction reveals organization of antenna and reaction center in photosynthetic bacteria

The photochemical phase of the bacteriochlorophyll fluorescence induction generated by rectangular shape of laser diode illumination was measured in different organization levels {whole cell, chromatophore and isolated reaction center protein) of carotenoidtess mutant of purple photosynthetic bacterium Rhodobacter sphaeroides R-26.1. While the antenna containing species showed large and positive variable fluorescence (fj relative to the constant (initial) fluorescence (Fa) {FJF^ ~ 4.5 in whole ceil), the isolated RC had smaller and negative change (FJF - -0.6). The variable fluorescence of the ceils increased steadily in the function of the age of the cultivated bacterium: FJF0 - 2 for young ceils and FJF0 - 4.5 fór old ceils while the rise time of the fluorescence induction remained constant (- 2 ms). In chromatophore, 7 times higher rate was measured than in isolated reaction center under identical experimental conditions. The results obtained under different conditions are interpreted by an extended version of the Lavergne-Trissl model where the simultaneously measured fluorescence inductions from the antenna and the RC can be separately expressed

Unstable semiquinone in photosynthetic reaction center

Ubiquinone can take up two electrons and two protons upon reduction and serves as essential redox cofactor in several proteins. Out of its 9 possible redox states, only Q and Q– are seen in the QA site and Q, Q– and QH2 in the Q8 site of the reaction center of photosynthetic bacterium Rhodobacter sphaeroides. The focus of our interest was the investigation of kinetic and energetic aspects of Q– stability in the Q8 binding site. Under physiological conditions, the semiquinone anion is very stable and it binds more tightly than Q or QH2. At high light intensity of continuous excitation, however, it binds poorly and favors release to the solution. We attribute the decrease of semiquinone affinity to conformational changes in the QB binding site upon repetitive and frequent charge separation (and subsequent very fast recombination) in the photochemically closed reaction center