Over the last two years, wavelet methods have shown themselves to be of considerable use to harmonic analysts and, in particular, advances have been made concerning their applications. The strength of wavelet methods lies in their ability to describe local phenomena more accurately than a traditional expansion in sines and cosines can. Thus, wavelets are ideal in many fields where an approach to transient behaviour is needed, for example, in considering acoustic or seismic signals, or in image processing. Yves Meyer stands the theory of wavelets firmly upon solid ground by basing his book on the fundamental work of Calderón, Zygmund and their collaborators. For anyone who would like an introduction to wavelets, this book will prove to be a necessary purchase.

Since their discovery as a substrate for ribonucleotide reductase (RNR), the role of thioredoxin (Trx) and glutaredoxin (Grx) has been largely extended through their regulatory function. Both proteins act by changing the structure and activity of a broad spectrum of target proteins, typically by modifying redox status. Trx and Grx are members of families with multiple and partially redundant genes. The number of genes clearly increased with the appearance of multicellular organisms, in part because of new types of Trx and Grx with orthologs throughout the animal and plant kingdoms. The function of Trx and Grx also broadened as cells achieved increased complexity, especially in the regulation arena. In view of these progressive changes, the ubiquitous distribution of Trx and the wide occurrence of Grx enable these proteins to serve as indicators of the evolutionary history of redox regulation. In so doing, they add a unifying element that links the diverse forms of life to one another in an uninterrupted continuum. It is anticipated that future research will embellish this continuum and further elucidate the properties of these proteins and their impact on biology. The new information will be important not only to our understanding of the role of Trx and Grx in fundamental cell processes but also to future societal benefits as the proteins find new applications in a range of fields.

Intracellular redox status is a critical parameter determining plant development in response to biotic and abiotic stress. Thioredoxin (TRX) and glutathione are key regulators of redox homeostasis, and the TRX and glutathione pathways are essential for postembryonic meristematic activities. Here, we show by associating TRX reductases (ntra ntrb) and glutathione biosynthesis (cad2) mutations that these two thiol reduction pathways interfere with developmental processes through modulation of auxin signaling. The triple ntra ntrb cad2 mutant develops normally at the rosette stage, undergoes the floral transition, but produces almost naked stems, reminiscent of the phenotype of several mutants affected in auxin transport or biosynthesis. In addition, the ntra ntrb cad2 mutant shows a loss of apical dominance, vasculature defects, and reduced secondary root production, several phenotypes tightly regulated by auxin. We further show that auxin transport capacities and auxin levels are perturbed in the mutant, suggesting that the NTR-glutathione pathways alter both auxin transport and metabolism. Analysis of ntr and glutathione biosynthesis mutants suggests that glutathione homeostasis plays a major role in auxin transport as both NTR and glutathione pathways are involved in auxin homeostasis.

Tight control of cellular redox homeostasis is essential for protection against oxidative damage and for maintenance of normal metabolism as well as redox signaling events. Under oxidative stress conditions, the tripeptide glutathione can switch from its reduced form (GSH) to oxidized glutathione disulfide (GSSG), and thus, forms an important cellular redox buffer. GSSG is normally reduced to GSH by 2 glutathione reductase (GR) isoforms encoded in the Arabidopsis genome, cytosolic GR1 and GR2 dual-targeted to chloroplasts and mitochondria. Measurements of total GR activity in leaf extracts of wild-type and 2 gr1 deletion mutants revealed that Ϸ65% of the total GR activity is attributed to GR1, whereas Ϸ35% is contributed by GR2. Despite the lack of a large share in total GR activity, gr1 mutants do not show any informative phenotype, even under stress conditions, and thus, the physiological impact of GR1 remains obscure. To elucidate its role in plants, glutathione-specific redox-sensitive GFP was used to dynamically measure the glutathione redox potential (E GSH) in the cytosol. Using this tool, it is shown that E GSH in gr1 mutants is significantly shifted toward more oxidizing conditions. Surprisingly, dynamic reduction of GSSG formed during induced oxidative stress in gr1 mutants is still possible, although significantly delayed compared with wild-type plants. We infer that there is functional redundancy in this critical pathway. Integrated biochemical and genetic assays identify the NADPH-dependent thioredoxin system as a backup system for GR1. Deletion of both, NADPH-dependent thioredoxin reductase A and GR1, prevents survival due to a pollen lethal phenotype.redox homeostasis ͉ redox imaging ͉ redox-sensitive GFP ͉ thioredoxin reductase

NADPH-dependent thioredoxin reductases (NTRs) are key regulatory enzymes determining the redox state of the thioredoxin system. The Arabidopsis thaliana genome has two genes coding for NTRs (NTRA and NTRB), both of which encode mitochondrial and cytosolic isoforms. Surprisingly, plants of the ntra ntrb knockout mutant are viable and fertile, although with a wrinkled seed phenotype, slower plant growth, and pollen with reduced fitness. Thus, in contrast with mammals, our data demonstrate that neither cytosolic nor mitochondrial NTRs are essential in plants. Nevertheless, in the double mutant, the cytosolic thioredoxin h3 is only partially oxidized, suggesting an alternative mechanism for thioredoxin reduction. Plant growth in ntra ntrb plants is hypersensitive to buthionine sulfoximine (BSO), a specific inhibitor of glutathione biosynthesis, and thioredoxin h3 is totally oxidized under this treatment. Interestingly, this BSO-mediated growth arrest is fully reversible, suggesting that BSO induces a growth arrest signal but not a toxic accumulation of activated oxygen species. Moreover, crossing ntra ntrb with rootmeristemless1, a mutant blocked in root growth due to strongly reduced glutathione synthesis, led to complete inhibition of both shoot and root growth, indicating that either the NTR or the glutathione pathway is required for postembryonic activity in the apical meristem.

Thioredoxins (Trx) and glutaredoxins (Grx) constitute families of thiol oxidoreductases. Our knowledge of Trx and Grx in plants has dramatically increased during the last decade. The release of the Arabidopsis genome sequence revealed an unexpectedly high number of Trx and Grx genes. The availability of several genomes of vascular and nonvascular plants allowed the establishment of a clear classification of the genes and the chronology of their appearance during plant evolution. Proteomic approaches have been developed that identified the putative Trx and Grx target proteins which are implicated in all aspects of plant growth, including basal metabolism, iron/sulfur cluster formation, development, adaptation to the environment, and stress responses. Analyses of the biochemical characteristics of specific Trx and Grx point to a strong specificity toward some target enzymes, particularly within plastidial Trx and Grx. In apparent contradiction with this specificity, genetic approaches show an absence of phenotype for most available Trx and Grx mutants, suggesting that redundancies also exist between Trx and Grx members. Despite this, the isolation of mutants inactivated in multiple genes and several genetic screens allowed the demonstration of the involvement of Trx and Grx in pathogen response, phytohormone pathways, and at several control points of plant development. Cytosolic Trxs are reduced by NADPH-thioredoxin reductase (NTR), while the reduction of Grx depends on reduced glutathione (GSH). Interestingly, recent development integrating biochemical analysis, proteomic data, and genetics have revealed an extensive crosstalk between the cytosolic NTR/Trx and GSH/Grx systems. This crosstalk, which occurs at multiple levels, reveals the high plasticity of the redox systems in plants.

ABSTRACT. Lp estimates for multilinear singular integrals generalizingCalderón's commutator integral are obtained. The methods introduced involve Fourier and Mellin analysis.

The Arabidopsis genome contains at least 18 genes encoding members of the 70-kilodalton heat shock protein (Hsp70) family, 14 in the DnaK subfamily and 4 in the Hsp110/SSE subfamily. While the Hsp70s are highly conserved, a phylogenetic analysis including all members of this family in Arabidopsis and in yeast indicates the homology of Hsp70s in the subgroups, such as those predicted to localize in the same subcellular compartment and those similar to the mammalian Hsp110 and Grp170. Gene structure and genome organization suggest duplication in the origin of some genes. The Arabidopsis hsp70s exhibit distinct expression profiles; representative genes of the subgroups are expressed at relatively high levels during specific developmental stages and under thermal stress.