Càlcul funcional: topologia, successions i continuïtat

Oferim als estudiants universitaris i als lectors interessats aquesta guia didàctica de la matemàtica universitària com a fruit dels nostres anys de docència de les matemàtiques a la Universitat. El resultat final ha esdevingut una col·lecció de setze petits volums agrupats en els dos mòduls d'Àlgebra Lineal i de Càlcul Infinitesimal. El present volum s’inicia amb un estudi de les nocions de la topologia de Rn , que creiem necessari per analitzar amb un mínim de rigor el concepte de continuïtat d’una funció, que tractem en aquest mateix volum, i el concepte de derivabilitat que analitzem en el volum següent. Així mateix, es realitza un estudi de les successions i sèries numèriques, noció que emprarem també per definir el límit d’una funció en un punt. Malgrat que incloem les definicions rigoroses d’alguns conceptes, hem volgut fugir deliberadament de l’excessiu rigor per donar prioritat a les idees intuïtives que ens poden ajudar a entendre la pràctica dels conceptes

Càlcul funcional: introducció a les funcions

Oferim als estudiants universitaris i als lectors interessats aquesta guia didàctica de la matemàtica universitària com a fruit dels nostres anys de docència de les matemàtiques a la Universitat. El resultat final ha esdevingut una col·lecció de setze petits volums agrupats en els dos mòduls d'Àlgebra Lineal i de Càlcul Infinitesimal. Pensem que l’estudi de les funcions incloses en aquest volum és interessant per fer un repàs de molts conceptes ja vistos en l’ensenyament secundari, però que considerem indispensables per entendre bé els nous temes de càlcul funcional que ens proposem desenvolupar en els propers volums

Functional analysis of rice bidirectional promoters

Bidirectional promoters regulate adjacent genes organized in a divergent fashion (head to head orientation). Several Reports pertaining to bidirectional promoters on a genomic scale exists in mammals. This work provides the essential background on theoretical and experimental work to carry out a genomic scale analysis of bidirectional promoters in plants. A computational study was performed to identify putative bidirectional promoters and the over-represented cis-regulatory motifs from three sequenced plant genomes: rice (Oryza sativa), Arabidopsis thaliana, and Populus trichocarpa using the Plant Cis-acting Regulatory DNA Elements (PLACE) and PLANT CARE databases. Over-represented motifs along with their possible function were described with the help of a few conserved representative putative bidirectional promoters from the three model plants. By doing so a foundation was laid for the experimental evaluation of bidirectional promoters in plants. A novel Agrobacterium tumefaciens mediated transient expression assay (AmTEA) was developed for young plants of different cereal species and the model dicot Arabidopsis thaliana. AmTEA was evaluated using five promoters (six constructs) and two reporter genes, gus and egfp. Efficacy and stability of AmTEA was compared with stable transgenics using the Arabidopsis DEAD-box RNA helicase family gene promoter. AmTEA was primarily developed to overcome the many problems associated with the development of transgenics and expression studies in plants. Finally a possible mechanism for the bidirectional activity of bidirectional promoters was highlighted. Deletion analysis using promoter-reporter gene constructs identified three rice promoters to be bidirectional. Regulatory elements located in the 5’- untranslated regions (UTR) of one of the genes of the divergent gene pair were found to be responsible for their bidirectional ctivity

A discrete-trial approach to the functional analysis of aggressive behaviour in two boys with autism

Intervention to reduce challenging behaviour may be enhanced when based on a prior functional analysis. The present study describes a discrete-trial approach for the functional analysis of aggressive behaviour in two boys with autism. Twenty brief assessment trials were conducted in the classroom by the teacher under each of three conditions (i.e., attention, task and tangible). The results showed a clear pattern to each child's aggressive behaviour and suggested logical intervention strategies, although the study is limited because it involved only two children. The discrete-trial approach would appear to represent a practical and ecologically valid technique for conducting a functional analysis of challenging behaviour in applied settings

Low frequency of CHEK2 1100delC allele in Australian multiple-case breast cancer families : functional analysis in heterozygous individuals

A protein-truncating variant of CHEK2, 1100delC, is associated with a moderate increase in breast cancer risk. We have determined the prevalence of this allele in index cases from 300 Australian multiple-case breast cancer families, 95% of which had been found to be negative for mutations in BRCA1 and BRCA2. Only two (0.6%) index cases heterozygous for the CHEK2 mutation were identified. All available relatives in these two families were genotyped, but there was no evidence of co-segregation between the CHEK2 variant and breast cancer. Lymphoblastoid cell lines established from a heterozygous carrier contained approximately 20% of the CHEK2 1100delC mRNA relative to wild-type CHEK2 transcript. However, no truncated CHK2 protein was detectable. Analyses of expression and phosphorylation of wild-type CHK2 suggest that the variant is likely to act by haploinsufficiency. Analysis of CDC25A degradation, a downstream target of CHK2, suggests that some compensation occurs to allow normal degradation of CDC25A. Such compensation of the 1100delC defect in CHEK2 might explain the rather low breast cancer risk associated with the CHEK2 variant, compared to that associated with truncating mutations in BRCA1 or BRCA2.

Multiple human single-stranded DNA binding proteins function in genome maintenance : structural, biochemical and functional analysis

DNA exists predominantly in a duplex form that is preserved via specific base pairing. This base pairing affords a considerable degree of protection against chemical or physical damage and preserves coding potential. However, there are many situations, e.g. during DNA damage and programmed cellular processes such as DNA replication and transcription, in which the DNA duplex is separated into two singlestranded DNA (ssDNA) strands. This ssDNA is vulnerable to attack by nucleases, binding by inappropriate proteins and chemical attack. It is very important to control the generation of ssDNA and protect it when it forms, and for this reason all cellular organisms and many viruses encode a ssDNA binding protein (SSB). All known SSBs use an oligosaccharide/oligonucleotide binding (OB)-fold domain for DNA binding. SSBs have multiple roles in binding and sequestering ssDNA, detecting DNA damage, stimulating strand-exchange proteins and helicases, and mediation of protein–protein interactions. Recently two additional human SSBs have been identified that are more closely related to bacterial and archaeal SSBs. Prior to this it was believed that replication protein A, RPA, was the only human equivalent of bacterial SSB. RPA is thought to be required for most aspects of DNA metabolism including DNA replication, recombination and repair. This review will discuss in further detail the biological pathways in which human SSBs function.

Functional analysis of missense variants in the TRESK (KCNK18) K+ channel

A loss of function mutation in the TRESK K2P potassium channel (KCNK18), has recently been linked with typical familial migraine with aura. We now report the functional characterisation of additional TRESK channel missense variants identified in unrelated patients. Several variants either had no apparent functional effect, or they caused a reduction in channel activity. However, the C110R variant was found to cause a complete loss of TRESK function, yet is present in both sporadic migraine and control cohorts, and no variation in KCNK18 copy number was found. Thus despite the previously identified association between loss of TRESK channel activity and migraine in a large multigenerational pedigree, this finding indicates that a single non-functional TRESK variant is not alone sufficient to cause typical migraine and highlights the genetic complexity of this disorder. Migraine is a common, disabling neurological disorder with a genetic, environmental and in some cases hormonal component. It is characterized by attacks of severe, usually unilateral and throbbing headache, can be accompanied by nausea, vomiting and photophobia and is clinically divided into two main subtypes, migraine with aura (MA) when a migraine is accompanied by transient and reversible focal neurological symptoms and migraine without aura (MO)1. The multifactorial and clinical heterogeneity of the disorder have considerably hindered the identification of common migraine susceptibility genes and most of our current understanding comes from the studies of familial hemiplegic migraine (FHM), a rare monogenic autosomal dominant form of MA2. So far, the three susceptibility genes that have been convincingly identified in FHM families all encode ion channels or transporters: CACNA1A encoding the α1 subunit of the Cav2.1 calcium channel3, SCN1A encoding the Nav1.1 sodium channel4 and ATP1A2 encoding the α2 subunit of the Na+/K+ pump5. It is believed that mutations in these genes may lead to increased efflux of glutamate and potassium in the synapse and thereby cause migraine by rendering the brain more susceptible to cortical spreading depression (CSD)6 which is thought to play a role in initiating a migraine attack7,8. However, these genes have not to date been implicated in common forms of migraine9. Nevertheless, current opinion suggests that typical migraine, like FHM, is also disorder of neuronal excitability, ion homeostasis and neurotransmitter release10,11,12. Mutations in the SLC4A4 gene encoding the sodium-bicarbonate cotransporter NBCe1, have recently been implicated in several different forms of migraine13, and a variety of genes involved in glutamate homeostasis (PGCP, MTDH14 and LRP115) and a cation channel (TRPM8)15 have also recently been implicated in migraine via genome-wide association studies. Ion channels are therefore highly likely to play an important role in the pathogenesis of typical migraine. TRESK (KCNK18), is a member of the two-pore domain (K2P) family of potassium channels involved in the control of cellular electrical excitability16. Regulation of TRESK activity by the calcium-dependent phosphatase calcineurin17, as well as its expression in dorsal root ganglia (DRG)18 and trigeminal ganglia (TG)19,20 has led to a proposed role for this channel in a variety of pain pathways. In a recent study, a frameshift mutation (F139Wfsx24) in TRESK was identified in a large multigenerational pedigree where it co-segregated perfectly with typical MA and a significant genome-wide linkage LOD score of 3.0. Furthermore, functional analysis revealed that this mutation caused a complete loss of TRESK function and that the truncated subunit was also capable of down regulating wild-type channel function. This therefore highlighted KCNK18 as potentially important candidate gene and suggested that TRESK dysfunction might play a possible role in the pathogenesis of familial migraine with visual aura20. Additional screening for KCNK18 mutations in unrelated sporadic migraine and control cohorts also identified a number of other missense variants; R10G, A34V, C110R, S231P and A233V20. The A233V variant was found only in the control cohort, whilst A34V was identified in a single Australian migraine proband for which family samples were not available, but it was not detected in controls. By contrast, the R10G, C110R, and S231P variants were found in both migraineurs and controls in both cohorts. In this study, we have investigated the functional effect of these variants to further probe the potential association of TRESK dysfunction with typical migraine.

Functional Analysis of MrpL55, Vig and Mat1 Acting at the Crossroad of Cell Cycle, Transcription and Metabolism Regulation

Cell proliferation, transcription and metabolism are regulated by complex partly overlapping signaling networks involving proteins in various subcellular compartments. The objective of this study was to increase our knowledge on such regulatory networks and their interrelationships through analysis of MrpL55, Vig, and Mat1 representing three gene products implicated in regulation of cell cycle, transcription, and metabolism. Genome-wide and biochemical in vitro studies have previously revealed MrpL55 as a component of the large subunit of the mitochondrial ribosome and demonstrated a possible role for the protein in cell cycle regulation. Vig has been implicated in heterochromatin formation and identified as a constituent of the RNAi-induced silencing complex (RISC) involved in cell cycle regulation and RNAi-directed transcriptional gene silencing (TGS) coupled to RNA polymerase II (RNAPII) transcription. Mat1 has been characterized as a regulatory subunit of cyclin-dependent kinase 7 (Cdk7) complex phosphorylating and regulating critical targets involved in cell cycle progression, energy metabolism and transcription by RNAPII. The first part of the study explored whether mRpL55 is required for cell viability or involved in a regulation of energy metabolism and cell proliferation. The results revealed a dynamic requirement of the essential Drosophila mRpL55 gene during development and suggested a function of MrpL55 in cell cycle control either at the G1/S or G2/M transition prior to cell differentiation. This first in vivo characterization of a metazoan-specific constituent of the large subunit of mitochondrial ribosome also demonstrated forth compelling evidence of the interconnection of nuclear and mitochondrial genomes as well as complex functions of the evolutionarily young metazoan-specific mitochondrial ribosomal proteins. In studies on the Drosophila RISC complex regulation, it was noted that Vig, a protein involved in heterochromatin formation, unlike other analyzed RISC associated proteins Argonaute2 and R2D2, is dynamically phosphorylated in a dsRNA-independent manner. Vig displays similarity with a known in vivo substrate for protein kinase C (PKC), human chromatin remodeling factor Ki-1/57, and is efficiently phosphorylated by PKC on multiple sites in vitro. These results suggest that function of the RISC complex protein Vig in RNAi-directed TGS and chromatin modification may be regulated through dsRNA-independent phosphorylation by PKC. In the third part of this study the role of Mat1 in regulating RNAPII transcription was investigated using cultured murine immortal fibroblasts with a conditional allele of Mat1. The results demonstrated that phosphorylation of the carboxy-terminal domain (CTD) of the large subunit of RNAPII in the heptapeptide YSPTSPS repeat in Mat-/- cells was over 10-fold reduced on Serine-5 and subsequently on Serine-2. Occupancy of the hypophosphorylated RNAPII in gene bodies was detectably decreased, whereas capping, splicing, histone methylation and mRNA levels were generally not affected. However, a subset of transcripts in absence of Mat1 was repressed and associated with decreased occupancy of RNAPII at promoters as well as defective capping. The results identify the Cdk7-CycH-Mat1 kinase submodule of TFIIH as a stimulatory non-essential regulator of transcriptional elongation and a genespecific essential factor for stable binding of RNAPII at the promoter region and capping. The results of these studies suggest important roles for both MrpL55 and Mat1 in cell cycle progression and their possible interplay at the G2/M stage in undifferentiated cells. The identified function of Mat1 and of TFIIH kinase complex in gene-specific transcriptional repression is challenging for further studies in regard to a possible link to Vig and RISC-mediated transcriptional gene silencing.

Functional Analysis of an Acid Adaptive DNA Adenine Methyltransferase from Helicobacter pylori 26695

HP0593 DNA-(N-6-adenine)-methyltransferase (HP0593 MTase) is a member of a Type III restriction-modification system in Helicobacter pylori strain 26695. HP0593 MTase has been cloned, overexpressed and purified heterologously in Escherichia coli. The recognition sequence of the purified MTase was determined as 5'-GCAG-3' and the site of methylation was found to be adenine. The activity of HP0593 MTase was found to be optimal at pH 5.5. This is a unique property in context of natural adaptation of H. pylori in its acidic niche. Dot-blot assay using antibodies that react specifically with DNA containing m6A modification confirmed that HP0593 MTase is an adenine-specific MTase. HP0593 MTase occurred as both monomer and dimer in solution as determined by gel-filtration chromatography and chemical-crosslinking studies. The nonlinear dependence of methylation activity on enzyme concentration indicated that more than one molecule of enzyme was required for its activity. Analysis of initial velocity with AdoMet as a substrate showed that two molecules of AdoMet bind to HP0593 MTase, which is the first example in case of Type III MTases. Interestingly, metal ion cofactors such as Co2+, Mn2+, and also Mg2+ stimulated the HP0593 MTase activity. Preincubation and isotope partitioning analyses clearly indicated that HP0593 MTase-DNA complex is catalytically competent, and suggested that DNA binds to the MTase first followed by AdoMet. HP0593 MTase shows a distributive mechanism of methylation on DNA having more than one recognition site. Considering the occurrence of GCAG sequence in the potential promoter regions of physiologically important genes in H. pylori, our results provide impetus for exploring the role of this DNA MTase in the cellular processes of H. pylori.

Functional analysis of conserved motifs in EcoP15I DNA methyltransferase

EcoP15I DNA methyltransferase recognizes the sequence 5'-CAGCAG-3' and transfers a methyl group to N-6 of the second adenine residue in the recognition sequence. All N-6 adenine methyltransferases contain two highly conserved sequences, FxGxG (motif I), postulated to form part of the S-adenosyl-L-methionine binding site and (D/N/S)PP(Y/F) (motif IV) involved in catalysis. We have altered the second glycine residue in motif I to arginine and serine, and substituted tyrosine in motif IV with tryptophan in EcoP15I DNA methyltransferase, using site-directed mutagenesis. The mutant enzymes were overexpressed, purified and characterized by biochemical methods. The mutations in motif I completely abolished AdoMet binding but left target DNA recognition unaltered. Although the mutation in motif IV resulted in loss of enzyme activity, we observed enhanced crosslinking of S-adenosyl-L-methionine and DNA. This implies that DNA and AdoMet binding sites are close to motif IV. Taken together, these results reinforce the importance of motif I in AdoMet binding and motif IV in catalysis. Additionally, limited proteolysis and UV crosslinking experiments with EcoP15I DNA methyltransferase imply that DNA binds in a cleft formed by two domains in the protein. Methylation protection analysis provides evidence for the fact that EcoP15I DNA MTase makes contacts in the major groove of its substrate DNA. Interestingly, hypermethylation of the guanine residue next to the target adenine residue indicates that the protein probably flips out the target adenine residue. (C) 1996 Academic Press Limited