Boundary value problems for second order linear difference equations: application to the computation of the inverse of generalized Jacobi matrices

We have named generalized Jacobi matrices to those that are practically tridiagonal, except for the two final entries and the two first entries of its first andits last row respectively. This class of matrices encompasses both standard Jacobiand periodic Jacobi matrices that appear in many contexts in pure and appliedmathematics. Therefore, the study of the inverse of these matrices becomes ofspecific interest. However, explicit formulas for inverses are known only in a fewcases, in particular when the coefficients of the diagonal entries are subjected tosome restrictions.We will show that the inverse of generalized Jacobi matrices can be raisedin terms of the resolution of a boundary value problem associated with a secondorder linear difference equation. In fact, recent advances in the study of lineardifference equations, allow us to compute the solution of this kind of boundaryvalue problems. So, the conditions that ensure the uniqueness of the solution ofthe boundary value problem leads to the invertibility conditions for the matrix,whereas that solutions for suitable problems provide explicitly the entries of theinverse matrix.Peer ReviewedPostprint (author's final draft

Nitric Oxide Controls Constitutive Freezing Tolerance in Arabidopsis by Attenuating the Levels of Osmoprotectants, Stress-Related Hormones and Anthocyanins

[EN] Plant tolerance to freezing temperatures is governed by endogenous constitutive components and environmental inducing factors. Nitric oxide (NO) is one of the endogenous components that participate in freezing tolerance regulation. A combined metabolomic and transcriptomic characterization of NO-deficient nia1,2noa1¿2 mutant plants suggests that NO acts attenuating the production and accumulation of osmoprotective and regulatory metabolites, such as sugars and polyamines, stress-related hormones, such as ABA and jasmonates, and antioxidants, such as anthocyanins and flavonoids. Accordingly, NO-deficient plants are constitutively more freezing tolerant than wild type plants.This work was supported by grants BIO2011-27526 and BIO2014-56067-P from the Spanish Ministry of Economy and Competitiveness and FEDER funds. We thank support and comments from Janice Jones and Danny Alexander (Metabolon Inc., USA) on metabolomic analyses.Costa-Broseta, Á.; Perea-Resa, C.; Castillo López Del Toro, MC.; Ruíz, MF.; Salinas, J.; Leon Ramos, J. (2018). Nitric Oxide Controls Constitutive Freezing Tolerance in Arabidopsis by Attenuating the Levels of Osmoprotectants, Stress-Related Hormones and Anthocyanins. Scientific Reports. 8. https://doi.org/10.1038/s41598-018-27668-8S8Janská, A., Marsík, P., Zelenková, S. & Ovesná, J. Cold stress and acclimation - what is important for metabolic adjustment? Plant Biol (Stuttg) 12, 395–405 (2010).Eremina, M., Rozhon, W. & Poppenberger, B. Hormonal control of cold stress responses in plants. Cell Mol Life Sci 73, 797–810 (2016).Winkel-Shirley, B. Biosynthesis of flavonoids and effects of stress. Curr Opin Plant Biol 5, 218–223 (2002).Cuevas, J. C. et al. Putrescine is involved in Arabidopsis freezing tolerance and cold acclimation by regulating abscisic acid levels in response to low temperature. Plant Physiol 148, 1094–105 (2008).Chen, M. & Thelen, J. J. Acyl-lipid desaturase 1 primes cold acclimation response in Arabidopsis. Physiol Plant 158, 11–22 (2016).Takahashi, D., Kawamura, Y. & Uemura, M. Cold acclimation is accompanied by complex responses of glycosylphosphatidylinositol (GPI)-anchored proteins in Arabidopsis. J Exp Bot 67, 5203–5215 (2016).van Buer, J., Cvetkovic, J. & Baier, M. Cold regulation of plastid ascorbate peroxidases serves as a priming hub controlling ROS signaling in Arabidopsis thaliana. BMC Plant Biol 16(1), 163 (2016).Zhao, M. G., Chen, L., Zhang, L. L. & Zhang, W. H. Nitric reductase dependent nitric oxide production is involved in cold acclimation and freezing tolerance in Arabidopsis. Plant Physiol 151, 755–767 (2009).Puyaubert, J. & Baudouin, E. New clues for a cold case: nitric oxide response to low temperature. Plant Cell & Environ 37, 2623–2630 (2014).Siddiqui, M. H., Al-Whaibi, M. H. & Basalah, M. O. Role of nitric oxide in tolerance of plants to abiotic stress. Protoplasma 248, 447–455 (2011).Arasimowicz-Jelonek, M. & Floryszak-Wieczorek, J. Nitric oxide: an effective weapon of the plant or the pathogen? Mol. Plant Pathol. 15, 406–416 (2014).Gupta, K. J., Fernie, A. R., Kaiser, W. M. & van Dongen, J. T. On the origins of nitric oxide. Trends Plant Sci. 16, 160–168 (2011).Mur, L. A. et al. Nitric oxide in plants: an assessment of the current state of knowledge. AoB Plants 5, pls052 (2013).Thomas, D. D. Breathing new life into nitric oxide signaling: A brief overview of the interplay between oxygen and nitric oxide. Redox Biol. 5, 225–33 (2015).Correa-Aragunde, N., Foresi, N. & Lamattina, L. Nitric oxide is a ubiquitous signal for maintaining redox balance in plant cells: regulation of ascorbate peroxidase as a case study. J. Exp. Bot. 66, 2913–2921 (2015).Groβ, F., Durner, J. & Gaupels, F. Nitric oxide, antioxidants and prooxidants in plant defence responses. Front. Plant Sci. 4, 419 (2013).Astier, J. & Lindermayr, C. Nitric oxide-dependent posttranslational modification in plants: an update. Int. J. Mol. Sci. 13, 15193–15208 (2012).Hess, D. T. & Stamler, J. S. Regulation by S-nitrosylation of protein post-translational modification. J. Biol. Chem. 287, 4411–4418 (2012).Guerra, D. D. & Callis, J. Ubiquitin on the move: the ubiquitin modification system plays diverse roles in the regulation of endoplasmic reticulum- and plasma membrane-localized proteins. Plant Physiol. 160, 56–64 (2012).Cantrel, C. et al. Nitric oxide participates in cold-responsive phosphosphingolipid formation and gene expression in Arabidopsis thaliana. New Phytol. 189, 415–427 (2011).Lozano-Juste, J. & León, J. Enhanced abscisic acid-mediated responses innia1,2noa1-2 triple mutant impaired in NIA/NR- and AtNOA1-dependent nitric oxide biosynthesis in Arabidopsis. Plant Physiol. 152, 891–903 (2010).Gibbs, D. J. et al. Nitric oxide sensing in plants is mediated by proteolytic control of group VII ERF transcription factors. Mol. Cell 53, 369–379 (2014).Lee, B. H., Henderson, D. A. & Zhu, J. K. The Arabidopsis cold-responsive transcriptome and its regulation by ICE1. Plant Cell 17, 3155–3175 (2005).Kilian, J. et al. The AtGenExpress global stress expression data set: protocols, evaluation and model data analysis of UV-B light, drought and cold stress responses. Plant J. 50, 347–363 (2007).Hu, Y., Jiang, L., Wang, F. & Yu, D. Jasmonate regulates the inducer of cbf expression-C-repeat binding factor/DRE binding factor1 cascade and freezing tolerance in Arabidopsis. Plant Cell 25, 2907–2924 (2013).Lee, H. G. & Seo, P. J. The MYB96-HHP module integrates cold and abscisic acid signaling to activate the CBF-COR pathway in Arabidopsis. Plant J. 82, 962–977 (2015).Kasukabe, Y. et al. Overexpression of spermidine synthase enhances tolerance to multiple environmental stresses and up-regulates the expression of various stress-regulated genes in transgenic Arabidopsis thaliana. Plant & Cell Physiol 45, 712–722 (2004).Korn, M., Peterek, S., Mock, H. P., Heyer, A. G. & Hincha, D. K. Heterosis in the freezing tolerance, and sugar and flavonoid contents of crosses between Arabidopsis thaliana accessions of widely varying freezing tolerance. Plant Cell & Environ. 31, 813–827 (2008).Guy, C., Kaplan, F., Kopka, J., Selbig, J. & Hincha, D. K. Metabolomics of temperature stress. Physiol. Plant. 132, 220–235 (2008).Berger, S. et al. Enzymatic and non enzymatic lipid peroxidation in leaf development. Biochem. Biophys. Acta 1533, 266–276 (2001).Yoshida, Y., Umeno, A. & Shichiri, M. Lipid peroxidation biomarkers for evaluating oxidative stress and assessing antioxidant capacity in vivo. J Clin. Biochem. Nutr. 52, 9–16 (2013).Catalá, R. et al. The Arabidopsis 14-3-3 protein RARE COLD INDUCIBLE 1A links low-temperature response and ethylene biosynthesis to regulate freezing tolerance and cold acclimation. Plant Cell 26, 3326–3342 (2014).Tähtiharju, S. & Palva, T. Antisense inhibition of protein phosphatase 2C accelerates cold acclimation in Arabidopsis thaliana. Plant J. 26, 461–470 (2001).Kawamura, Y. & Uemura, M. Mass spectrometric approach for identifying putative plasma membrane proteins of Arabidopsis leaves associated with cold acclimation. Plant J. 36, 141–154 (2003).Xin, Z. & Browse, J. Eskimo1 mutants of Arabidopsis are constitutively freezing-tolerant. Proc. Natl. Acad. Sci. USA 95, 7799–7804 (1998).Nanjo, T. et al. Antisense suppression of proline degradation improves tolerance to freezing and salinity in Arabidopsis thaliana. FEBS Lett. 461, 205–210 (1999).Zuther, E., Schulz, E., Childs, L. H. & Hincha, D. K. Clinal variation in the non-acclimated and cold-acclimated freezing tolerance of Arabidopsis thaliana accessions. Plant Cell & Environ. 35, 1860–1878 (2012).Alcázar, R., García-Martínez, J. L., Cuevas, J. C., Tiburcio, A. F. & Altabella, T. Overexpression of ADC2 in Arabidopsis induces dwarfism and late-flowering through GA deficiency. Plant J. 43, 425–436 (2005).Alet, A. I. et al. Putrescine accumulation in Arabidopsis thaliana transgenic lines enhances tolerance to dehydration and freezing stress. Plant Signal. & Behav. 6, 278–286 (2011).Nägele, T., Stutz, S., Hörmiller, I. I. & Heyer, A. G. Identification of a metabolic bottleneck for cold acclimation in Arabidopsis thaliana. Plant J. 72, 102–114 (2012).Krol, M. et al. Low-temperature stress and photoperiod affect an increased tolerance to photoinhibition in Pinus banksiana seedlings. Canadian Journal of Botany 73, 1119–1127 (1995).Harvaux, M. & Kloppstech, K. The protective functions of carotenoid and flavonoid pigments against excess visible radiation at chilling temperature investigated in Arabidopsis npq and tt mutants. Planta 213, 953–966 (2001).Schulz, E., Tohge, T., Zuther, E., Fernie, A. R. & Hincha, D. K. Flavonoids are determinants of freezing tolerance and cold acclimation in Arabidopsis thaliana. Sci. Rep. 6, 34027 (2016).Llorente, F., Oliveros, J. C., Martínez-Zapater, J. M. & Salinas, J. A freezing-sensitive mutant of Arabidopsis, frs1, is a new aba3 allele. Planta 211, 648–655 (2000).Lozano-Juste, J., Colom-Moreno, R. & León, J. In vivo protein tyrosine nitration in Arabidopsis thaliana. J. Exp. Bot. 62, 3501–3517.Gill, S. S. & Tuteja, N. Reactive oxygen species and antioxidant machinery in abiotic stress tolerance in crop plants. Plant Physiol. Biochem. 48, 909–930 (2010).Begara-Morales, J. C. et al. Antioxidant Systems are Regulated by Nitric Oxide-Mediated Post-translational Modifications (NO-PTMs). Front. Plant Sci. 7, 152 (2016).Castillo, M. C. & León, J. Expression of the beta-oxidation gene 3-ketoacyl-CoA thiolase 2 (KAT2) is required for the timely onset of natural and dark-induced leaf senescence in Arabidopsis. J. Exp. Bot. 59, 2171–2179 (2008).Guo, F. Q., Okamoto, M. & Crawford, N. M. Identification of a plant nitric oxide synthase gene involved in hormonal signaling. Science 302, 100–103 (2003).Solfanelli, C., Poggi, A., Loreti, E., Alpi, A. & Perata, P. Sucrose-specific induction of the anthocyanin biosynthetic pathway in Arabidopsis. Plant Physiol. 140, 637–646 (2006).Seo, M., Jikumaru, Y. & Kamiya, Y. Profiling of Hormones and Related Metabolites in Seed Dormancy and Germination Studies. Meth. Mol. Biol. 773, 99–111 (2011)

Oxidation of ruthenium oxide deposits by ozone

During a hypothetical severe accident on a nuclear Pressurized Water Reactor (PWR), the formation of highly radiotoxic RuO4(g) may occur in the reactor containment building, resulting from the interactions of ruthenium oxide deposits with the oxidising medium induced by air radiolysis. Consequently, there is a risk that the gaseous ruthenium tetroxide could be dispersed into the environment through containment leakages; therefore data concerning the behaviour of ruthenium oxide deposits is of primary importance for safety studies. An experiment has been designed to study the interactions of ruthenium oxide deposits with ozone, formed by air radiolysis. Experimental results have shown that the oxidation reaction leading to the formation of RuO4(g) occurred to a large extent. An oxidation kinetic rate law has been determined, in dry and moist air, for ruthenium deposited onto painted substrates, representative of the inner surfaces of PWR's. This law, combined with tetroxide stability data [1], will allow a first evaluation of ruthenium revolatilisation phenomenon, possibly occurring in the containment during a severe accident. © by Oldenbourg Wissenschaftsverlag

Study of RuO4 decomposition in dry and moist air

During a hypothetical severe nuclear accident on a pressurized water reactor (PWR), it is of primary importance to assess potential radionuclide release into the environment, and thus to better understand the volatile ruthenium tetroxide stability, in the containment building, due to its high radiotoxicity. The stability of RuO4 (g) in dry and moist air, under conditions representative of a PWR containment building, is investigated. RuO4 decomposition occurs in bulk gas phase, without any specific affinity with surfaces. The kinetic rate law of RuO4 reduction is found to be dependent on the presence of steam. The humidity seems to play a catalytic role, as well as the presence of ruthenium dioxide deposits. The temperature is also a key parameter. In the presence of steam, the half-life times of RuO4 are found to be respectively of 5 h and 9 h at 90°C and 40°C. A chemical reaction scheme consistent with the experimental observations is proposed. © by Oldenbourg Wissenschaftsverlag

Source term assessment with ASTEC and associated uncertainty analysis using SUNSET tool

International audienceSeveral accidental scenarios have been simulated using the ASTEC integral IRSN-GRS code for a French 1300 MWe PWR, including several break sizes or locations, highlighting the effect of safety systems and of iodine chemistry in the reactor coolant system (RCS) and in the containment on iodine source term evaluations. Iodine chemistry in the RCS and in the containment is still subject to significant uncertainties and it is thus studied in on-going RandD programs. To assess the impact of uncertainties, ASTEC has been coupled to the IRSN uncertainty propagation and sensitivity analysis tool SUNSET. Focusing on a loss of feed-water of steam generator accident, ASTEC/SUNSET calculations have been performed to assess the effect of remaining uncertainties relative to iodine behaviour on the source term. Calculations show that the postulated lack of knowledge may impact the iodine source term in the environment by at least one decade, confirming the importance of the on-going RandD programs to improve the knowledge on iodine chemistry. © 2013 Elsevier B.V

Filtration tests of gaseous ruthenium tetroxide by sand bed and metallic filters

International audienceThis work presents laboratory tests on gaseous RuO4 filtration carried out at IRSN in Cadarache. The objective is to determine if gaseous ruthenium tetroxide can be trapped by metallic filter and sand bed filter, both elements being used in filtered containment venting systems implemented on French pressurized water reactors. The results show no ruthenium tetroxide trapping by physical or chemical adsorption but certain retention is observed resulting from its thermal decomposition into solid ruthenium dioxide. A thermodynamic analysis of the system tends to confirm this conclusion. Chemical stability of RuO4(g) has to be considered as it strongly impacts potential filtration and so potential releases. © 2019, Akadémiai Kiadó, Budapest, Hungary

Theoretical investigation of thermochemical properties of cesium borates species

International audienceThe coupled cluster single-double and perturbative triple (CCSD(T)) approach within highly correlated wave functions has been performed to better understand the thermochemical properties of gaseous cesium borates. Several corrections were added for core-valence correlation and relativistic effects. Structural parameters have been optimized with the B3LYP/aug-cc-pVTZ level of theory. The standard molar entropies and heat capacities at constant pressure have been also determined at the same level of theory. Δ f H° 298K have been obtained for the studied cesium borates species using a set of three reactions. The standard enthalpies at 298 K for CsBO 2 and Cs 2 B 2 O 4 are estimated to be (−689.0 ± 3.8) and (−1578.5 ± 7.0) kJ mol −1 , respectively. They are in good agreement with available literature data. Numerical simulations show that in a nuclear context, CsBO 2 will be formed preferentially to CsOH in steam atmosphere for high temperature. © 2019 Elsevier B.V

ASTEC V2 severe accident integral code Fission product modelling and validation

International audienceOne main goal of the severe accident integral code ASTEC V2, jointly developed since almost more than 15 years by IRSN and GRS, is to simulate the overall behaviour of fission products (FP) in a damaged nuclear facility. ASTEC applications are source term determinations, level 2 Probabilistic Safety Assessment (PSA2) studies including the determination of uncertainties, accident management studies and physical analyses of FP experiments to improve the understanding of the phenomenology. ASTEC is a modular code and models of a part of the phenomenology are implemented in each module the release of FPs and structural materials from degraded fuel in the ELSA module; the transport through the reactor coolant system approximated as a sequence of control volumes in the SOPHAEROS module; and the radiochemistry inside the containment nuclear building in the IODE module. Three other modules, CPA, ISODOP and DOSE, allow respectively computing the deposition rate of aerosols inside the containment, the activities of the isotopes as a function of time, and the gaseous dose rate which is needed to model radiochemistry in the gaseous phase. In ELSA, release models are semi-mechanistic and have been validated for a wide range of experimental data, and noticeably for VERCORS experiments. For SOPHAEROS, the models can be divided into two parts vapour phase phenomena and aerosol phase phenomena. For IODE, iodine and ruthenium chemistry are modelled based on a semi-mechanistic approach, these FPs can form some volatile species and are particularly important in terms of potential radiological consequences. The models in these 3 modules are based on a wide experimental database, resulting for a large part from international programmes, and they are considered at the state of the art of the RandD knowledge. This paper illustrates some FPs modelling capabilities of ASTEC and computed values are compared to some experimental results, which are parts of the validation matrix. © 2014 Elsevier B.V