Jumping numbers of a simple complete ideal in a two-dimensional regular local ring

The multiplier ideals of an ideal in a regular local ring form a family of ideals parametrized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.

Plasmids and aromatic degradation in Sphingomonas for bioremediation : Aromatic ring cleavage genes in soil and rhizosphere

Microbial degradation pathways play a key role in the detoxification and the mineralization of polyaromatic hydrocarbons (PAHs), which are widespread pollutants in soil and constituents of petroleum hydrocarbons. In microbiology the aromatic degradation pathways are traditionally studied from single bacterial strains with capacity to degrade certain pollutant. In soil the degradation of aromatics is performed by a diverse community of micro-organisms. The aim of this thesis was to study biodegradation on different levels starting from a versatile aromatic degrader Sphingobium sp. HV3 and its megaplasmid, extending to revelation of diversity of key catabolic enzymes in the environment and finally studying birch rhizoremediation in PAH-polluted soil. To understand biodegradation of aromatics on bacterial species level, the aromatic degradation capacity of Sphingobium sp. HV3 and the role of the plasmid pSKY4, was studied. Toluene, m-xylene, biphenyl, fluorene, phenanthrene were detected as carbon and energy sources of the HV3 strain. Tn5 transposon mutagenesis linked the degradation capacity of toluene, m-xylene, biphenyl and naphthalene to the pSKY4 plasmid and qPCR expression analysis showed that plasmid extradiol dioxygenases genes (bphC and xylE) are inducted by phenanthrene, m-xylene and biphenyl whereas the 2,4-dichlorophenoxyacetic acid herbicide induced the chlorocatechol 1,2-dioxygenase gene (tfdC) from the ortho-pathway. A method to study upper meta-pathway extradiol dioxygenase gene diversity in soil was developed. The extradiol dioxygenases catalyse cleavage of the aromatic ring between a hydroxylated carbon and an adjacent non-hydroxylated carbon (meta-cleavage). A high diversity of extradiol dioxygenases were detected from polluted soils. The detected extradiol dioxygenases showed sequence similarity to known catabolic genes of Alpha-, Beta-, and Gammaproteobacteria. Five groups of extradiol dioxygenases contained sequences with no close homologues in the database, representing novel genes. In rhizoremediation experiment with birch (Betula pendula) treatment specific changes of extradiol dioxygenase communities were shown. PAH pollution changed the bulk soil extradiol dioxygenase community structure and birch rhizosphere contained a more diverse extradiol dioxygenase community than the bulk soil showing a rhizosphere effect. The degradation of pyrene in soil was enhanced with birch seedlings compared to soil without birch. The complete 280,923 kb nucleotide sequence of pSKY4 plasmid was determined. The open reading frames of pSKY4 were divided into putative conjugative transfer, aromatic degradation, replication/maintaining and transposition/integration function-encoding proteins. Aromatic degradation orfs shared high similarity to corresponding genes in pNL1, a plasmid from the deep subsurface strain Novosphingobium aromaticivorans F199. The plasmid backbones were considerably more divergent with lower similarity, which suggests that the aromatic pathway has functioned as a plasmid independent mobile genetic element. The functional diversity of microbial communities in soil is still largely unknown. Several novel clusters of extradiol dioxygenases representing catabolic bacteria, whose function, biodegradation pathways and phylogenetic position is not known were amplified with single primer pair from polluted soils. These extradiol dioxygenase communities were shown to change upon PAH pollution, which indicates that their hosts function in PAH biodegradation in soil. Although the degradation pathways of specific bacterial species are substantially better depicted than pathways in situ, the evolution of degradation pathways for the xenobiotic compounds is largely unknown. The pSKY4 plasmid contains aromatic degradation genes in putative mobile genetic element causing flexibility/instability to the pathway. The localisation of the aromatic biodegradation pathway in mobile genetic elements suggests that gene transfer and rearrangements are a competetive advantage for Sphingomonas bacteria in the environment.

Plant guard cell anion channel SLAC1 regulates stomatal closure

Plants are rooted to their growth place; therefore it is important that they react adequately to changes in environmental conditions. Stomatal pores, which are formed of a pair of guard cells in leaf epidermis, regulate plant gas-exchange. Importantly, guard cells protect the plant from desiccation in drought conditions by reducing the aperture of the stomatal pore. They serve also as the first barrier against the major air pollutant ozone, but the behaviour of guard cells during ozone exposure has not been sufficiently addressed. Aperture of the stomatal pore is regulated by the influx and efflux of osmotically active ions via ion channels and transporters across the guard cell membrane, however the molecular identity of guard cell plasma membrane anion channel has remained unknown. In the frame of this study, guard cell behaviour during ozone exposure was studied using the newly constructed Arabidopsis whole-rosette gas-exchange system. Ozone induced a Rapid Transient Decrease (RTD) in stomatal conductance within 10 min from the start of exposure, which was followed by a recovery in the conductance within the next 40 min. The decrease in stomatal conductance was dependent on the applied ozone concentration. Three minutes of ozone exposure was sufficient to induce RTD and further ozone application during the closure-recovery process had no effect on RTD, demonstrating that the whole process is programmed within the first three minutes. To address the molecular components responsible for RTD, the ozone response was measured in 59 different Arabidopsis mutants involved in guard cell signalling. Four of the tested mutants slac1 (originally rcd3), ost1, abi1-1 and abi2-1 lacked RTD completely. As the ozone sensitive mutant slac1 lacked RTD, the next aim of this study was to identify and characterize SLAC1. SLAC1 was shown to be a central regulator in response to all major factors regulating guard cell aperture: CO2, light/darkness transitions, ozone, relative air humidity, ABA, NO, H2O2, and extracellular Ca2+. It encodes the first guard cell plasma membrane slow type anion channel to be identified at the molecular level. Interestingly, the rapid type anion conductance was intact in slac1 mutant plants. For activation, SLAC1 needs to be phosphorylated. Protein kinase OST1 was shown to phosphorylate several amino acids in the N-terminal tail of SLAC1, Ser120 was one of its main targets, which led to SLAC1 activation. The lack of RTD in type 2C protein phosphatase mutants abi1-1 and abi2-1, suggests that these proteins have a regulatory role in ozoneinduced activation of the slow type anion channel.