Local stability implies global stability for the 2-dimensional Ricker map

Consider the difference equation $x_{k+1}=x_k e^{\alpha-x_{n-d}}$ where $\alpha$ is a positive parameter and d is a non-negative integer. The case d = 0 was introduced by W.E. Ricker in 1954. For the delayed version d >= 1 of the equation S. Levin and R. May conjectured in 1976 that local stability of the nontrivial equilibrium implies its global stability. Based on rigorous, computer aided calculations and analytical tools, we prove the conjecture for d = 1.Comment: for associated C++ program, mathematica worksheet and output, see http://www.math.u-szeged.hu/~krisztin/ricke

Structurally flexible macro-organization of the pigment-protein complexes of the diatom Phaeodactylum tricornutum

By means of circular dichroism (CD) spectroscopy, we have characterized the organization of the photosynthetic complexes of the diatom Phaeodactylum tricornutum at different levels of structural complexity: in intact cells, isolated thylakoid membranes and purified fucoxanthin chlorophyll protein (FCP) complexes. We found that the CD spectrum of whole cells was dominated by a large band at (+)698 nm, accompanied by a long tail from differential scattering, features typical for psi-type (polymerization or salt-induced) CD. The CD spectrum additionally contained intense (-)679 nm, (+)445 nm and (-)470 nm bands, which were also present in isolated thylakoid membranes and FCPs. While the latter two bands were evidently produced by excitonic interactions, the nature of the (-)679 nm band remained unclear. Electrochromic absorbance changes also revealed the existence of a CD-silent long-wavelength (∼545 nm) absorbing fucoxanthin molecule with very high sensitivity to the transmembrane electrical field. In intact cells the main CD band at (+)698 nm appeared to be associated with the multilamellar organization of the thylakoid membranes. It was sensitive to the osmotic pressure and was selectively diminished at elevated temperatures and was capable of undergoing light-induced reversible changes. In isolated thylakoid membranes, the psi-type CD band, which was lost during the isolation procedure, could be partially restored by addition of Mg-ions, along with the maximum quantum yield and the non-photochemical quenching of singlet excited chlorophyll a, measured by fluorescence transients. © 2007 Springer Science+Business Media B.V

Nonlinear photonics properties of porphyrins nanocomposites and self-assembled porphyrins

Two major reasons limit porphyrins photonic applications: (i) the difficulty of handling them in liquid solutions and (ii) their degradation with long exposure to light. This necessitates the use of appropriate solid matrices to host the porphyrin compounds such as Nafion (117), a stable and inert ion exchange polymer. The first part of this publication confirms such a possibility. In addition to their effective NLO properties, an enhancement of the Soret and Q-bands absorbance width have been observed by blending three different porphyrin molecules in the Nafion column matrix membrane. This is an important development towards achieving efficient photon-harvesting medium for possible application in photonic devices. The second part of this contribution reports on the self-assembly/molecular recognition of a specific class of porphyrins giving rise to tubular nano-systems with potential THG nonlinear properties

Functional heterogeneity of the fucoxanthins and fucoxanthin-chlorophyll proteins in diatom cells revealed by their electrochromic response and fluorescence and linear dichroism spectra

In this work, by analyzing the electrochromic transient spectra, the 77 K fluorescence emission and excitation, as well as the linear dichroism (LD) and circular dichroism (CD) spectra of low-light (LL) and high-light (HL) grown Phaeodactylum tricornutum cells, we show that the fucoxanthins (Fx) and fucoxanthin-chlorophyll proteins (FCP) exhibit marked functional heterogeneity. Electrochromic transients reveal that LL and HL cells differ substantially in their relative contents of two Fx forms, which absorb at 501 and 550 nm; they exhibit distinct LD signals but are CD silent. Fluorescence emission and excitation spectra at 77 K reveal that although both forms efficiently transfer excitation energy to Chl a, the red form feeds somewhat more energy to photosystem II than to photosystem I. Similar data obtained in Cyclotella meneghiniana cells suggest that the heterogeneity of the FCP pool, with different Fx forms, plays a role in the regulation of energy utilization in FCP-containing organisms. © 2010 Elsevier B.V. All rights reserved

Chloroplast remodeling during state transitions in Chlamydomonas reinhardtii as revealed by noninvasive techniques in vivo

International audiencePlants respond to changes in light quality by regulating the absorption capacity of their photosystems. These short-term adaptations use redox-controlled, reversible phosphorylation of the light-harvesting complexes (LHCIIs) to regulate the relative absorption cross-section of the two photosystems (PSs), commonly referred to as state transitions. It is acknowledged that state transitions induce substantial reorganizations of the PSs. However, their consequences on the chloroplast structure are more controversial. Here, we investigate how state transitions affect the chloroplast structure and function using complementary approaches for the living cells of Chlamydomonas reinhardtii. Using small-angle neutron scattering, we found a strong periodicity of the thylakoids in state 1, with characteristic repeat distances of ∼200 Å, which was almost completely lost in state 2. As revealed by circular dichroism, changes in the thylakoid periodicity were paralleled by modifications in the long-range order arrangement of the photosynthetic complexes, which was reduced by ∼20% in state 2 compared with state 1, but was not abolished. Furthermore, absorption spectroscopy reveals that the enhancement of PSI antenna size during state 1 to state 2 transition (∼20%) is not commensurate to the decrease in PSII antenna size (∼70%), leading to the possibility that a large part of the phosphorylated LHCIIs do not bind to PSI, but instead form energetically quenched complexes, which were shown to be either associated with PSII supercomplexes or in a free form. Altogether these noninvasive in vivo approaches allow us to present a more likely scenario for state transitions that explains their molecular mechanism and physiological consequences

Plants lacking the main light-harvesting complex retain photosystem II macro-organization

Photosystem II (PSII) is a key component of photosynthesis, the process of converting sunlight into the chemical energy of life. In plant cells, it forms a unique oligomeric macrostructure in membranes of the chloroplasts. Several light-harvesting antenna complexes are organized precisely in the PSII macrostructure—the major trimeric complexes (LHCII) that bind 70% of PSII chlorophyll and three minor monomeric complexes—which together form PSII supercomplexes. The antenna complexes are essential for collecting sunlight and regulating photosynthesis, but the relationship between these functions and their molecular architecture is unresolved. Here we report that antisense Arabidopsis plants lacking the proteins that form LHCII trimers have PSII supercomplexes with almost identical abundance and structure to those found in wild-type plants. The place of LHCII is taken by a normally minor and monomeric complex, CP26, which is synthesized in large amounts and organized into trimers. Trimerization is clearly not a specific attribute of LHCII. Our results highlight the importance of the PSII macrostructure: in the absence of one of its main components, another protein is recruited to allow it to assemble and function

Linear dichroism and circular dichroism in photosynthesis research

The efficiency of photosynthetic light energy conversion depends largely on the molecular architecture of the photosynthetic membranes. Linear- and circular-dichroism (LD and CD) studies have contributed significantly to our knowledge of the molecular organization of pigment systems at different levels of complexity, in pigment–protein complexes, supercomplexes, and their macroassemblies, as well as in entire membranes and membrane systems. Many examples show that LD and CD data are in good agreement with structural data; hence, these spectroscopic tools serve as the basis for linking the structure of photosynthetic pigment–protein complexes to steady-state and time-resolved spectroscopy. They are also indispensable for identifying conformations and interactions in native environments, and for monitoring reorganizations during photosynthetic functions, and are important in characterizing reconstituted and artificially constructed systems. This educational review explains, in simple terms, the basic physical principles, and theory and practice of LD and CD spectroscopies and of some related quantities in the areas of differential polarization spectroscopy and microscopy

Diurnal Fluctuations in the Content and Functional Properties of the Light Harvesting Chlorophyll a/b Complex in Thylakoid Membranes:Correlation with the Diurnal Rhythm of the mRNA Level

Diurnal fluctuations were observed in the content and some structural and functional properties of the light-harvesting chlorophyll (Chl) a/b pigment-protein complex of photosystem II (LHCII) in young developing wheat (Triticum aestivum) leaves grown under 16 hours light/8 hours dark illumination regime. The fluctuations could be correlated with the diurnal oscillation in the level of mRNA for LHCII. The most pronounced changes occurred in the basal segments of the leaves. They were weaker or hardly discernible in the middle and tip segments. As judged from the diurnal variations of the Chl-a/Chl-b molar ratio, the LHCII content of the thylakoid membranes peaked around 2 pm. This can be accounted for by the cumulative effect of the elevated level of mRNA in the morning and early afternoon. In the basal segment, the extent of the fluctuation in the LHCII content was approximately 25%, as determined from gel electrophoresis ("green gels"). The amplitude of the principal bands of the circular dichroism (CD) spectra of isolated chloroplasts paralleled the changes in the LHCII content. Our circular dichroism data suggest that the newly synthesized LHCII complexes are incorporated into the existing helically organized macrodomains of the pigment-protein complexes or themselves form such macrodomains in the thylakoid membranes. Chl-a fluorescence induction kinetics also showed diurnal variations especially in the basal segments of the leaves. This most likely indicates fluctuations in the ability of membranes to undergo "state transitions." These observations suggest a physiological role of diurnal rhythm of mRNA for LHCII in young developing leaves

The Arabidopsis Thylakoid Chloride Channel AtCLCe Functions in Chloride Homeostasis and Regulation of Photosynthetic Electron Transport.

Chloride ions can be translocated across cell membranes through Cl(-) channels or Cl(-)/H(+) exchangers. The thylakoid-located member of the Cl(-) channel CLC family in Arabidopsis thaliana (AtCLCe) was hypothesized to play a role in photosynthetic regulation based on the initial photosynthetic characterization of clce mutant lines. The reduced nitrate content of Arabidopsis clce mutants suggested a role in regulation of plant nitrate homeostasis. In this study, we aimed to further investigate the role of AtCLCe in the regulation of ion homeostasis and photosynthetic processes in the thylakoid membrane. We report that the size and composition of proton motive force were mildly altered in two independent Arabidopsis clce mutant lines. Most pronounced effects in the clce mutants were observed on the photosynthetic electron transport of dark-adapted plants, based on the altered shape and associated parameters of the polyphasic OJIP kinetics of chlorophyll a fluorescence induction. Other alterations were found in the kinetics of state transition and in the macro-organization of photosystem II supercomplexes, as indicated by circular dichroism measurements. Pre-treatment with KCl but not with KNO3 restored the wild-type photosynthetic phenotype. Analyses by transmission electron microscopy revealed a bow-like arrangement of the thylakoid network and a large thylakoid-free stromal region in chloroplast sections from the dark-adapted clce plants. Based on these data, we propose that AtCLCe functions in Cl(-) homeostasis after transition from light to dark, which affects chloroplast ultrastructure and regulation of photosynthetic electron transport

Digalactosyl-diacylglycerol-deficiency lowers the thermal stability of thylakoid membranes

We investigated the effects of digalactosyl-diacylglycerol (DGDG) on the organization and thermal stability of thylakoid membranes, using wild-type Arabidopsis thaliana and the DGDG-deficient mutant, dgd1. Circular-dichroism measurements reveal that DGDG-deficiency hampers the formation of the chirally organized macrodomains containing the main chlorophyll a/b light-harvesting complexes. The mutation also brings about changes in the overall chlorophyll fluorescence lifetimes, measured in whole leaves as well as in isolated thylakoids. As shown by time-resolved measurements, using the lipophylic fluorescence probe Merocyanine 540 (MC540), the altered lipid composition affects the packing of lipids in the thylakoid membranes but, as revealed by flash-induced electrochromic absorbance changes, the membranes retain their ability for energization. Thermal stability measurements revealed more significant differences. The disassembly of the chiral macrodomains around 55°C, the thermal destabilization of photosystem I complex at 61°C as detected by green gel electrophoresis, as well as the sharp drop in the overall chlorophyll fluorescence lifetime above 45°C (values for the wild type—WT) occur at 4–7°C lower temperatures in dgd1. Similar differences are revealed in the temperature dependence of the lipid packing and the membrane permeability: at elevated temperatures MC540 appears to be extruded from the dgd1 membrane bilayer around 35°C, whereas in WT, it remains lipid-bound up to 45°C and dgd1 and WT membranes become leaky around 35 and 45°C, respectively. It is concluded that DGDG plays important roles in the overall organization of thylakoid membranes especially at elevated temperatures