p-adic L functions and trivial zeroes

The following is adapted from the notes for the lecture. It announces results and conjectures about values of the p-adic L function of the symmetric square of an elliptic curve.

A human Cds1-related kinase that functions downstream of ATM protein in the cellular response to DNA damage

Checkpoints maintain the order and fidelity of the eukaryotic cell cycle, and defects in checkpoints contribute to genetic instability and cancer. Much of our current understanding of checkpoints comes from genetic studies conducted in yeast. In the fission yeast Schizosaccharomyces pombe (Sp), SpRad3 is an essential component of both the DNA damage and DNA replication checkpoints. The SpChk1 and SpCds1 protein kinases function downstream of SpRad3. SpChk1 is an effector of the DNA damage checkpoint and, in the absence of SpCds1, serves an essential function in the DNA replication checkpoint. SpCds1 functions in the DNA replication checkpoint and in the S phase DNA damage checkpoint. Human homologs of both SpRad3 and SpChk1 but not SpCds1 have been identified. Here we report the identification of a human cDNA encoding a protein (designated HuCds1) that shares sequence, structural, and functional similarity to SpCds1. HuCds1 was modified by phosphorylation and activated in response to ionizing radiation. It was also modified in response to hydroxyurea treatment. Functional ATM protein was required for HuCds1 modification after ionizing radiation but not after hydroxyurea treatment. Like its fission yeast counterpart, human Cds1 phosphorylated Cdc25C to promote the binding of 14-3-3 proteins. These findings suggest that the checkpoint function of HuCds1 is conserved in yeast and mammals.

Cooperative functions of the reaper and head involution defective genes in the programmed cell death of Drosophila central nervous system midline cells

In Drosophila, the chromosomal region 75C1–2 contains at least three genes, reaper (rpr), head involution defective (hid), and grim, that have important functions in the activation of programmed cell death. To better understand how cells are killed by these genes, we have utilized a well defined set of embryonic central nervous system midline cells that normally exhibit a specific pattern of glial cell death. In this study we show that both rpr and hid are expressed in dying midline cells and that the normal pattern of midline cell death requires the function of multiple genes in the 75C1–2 interval. We also utilized the P[UAS]/P[Gal4] system to target expression of rpr and hid to midline cells. Targeted expression of rpr or hid alone was not sufficient to induce ectopic midline cell death. However, expression of both rpr and hid together rapidly induced ectopic midline cell death that resulted in axon scaffold defects characteristic of mutants with abnormal midline cell development. Midline-targeted expression of the baculovirus p35 protein, a caspase inhibitor, blocked both normal and ectopic rpr- and hid-induced cell death. Taken together, our results suggest that rpr and hid are expressed together and cooperate to induce programmed cell death during development of the central nervous system midline.

Gene Knockouts Reveal Separate Functions for Two Cytoplasmic Dyneins in Tetrahymena thermophila

In many organisms, there are multiple isoforms of cytoplasmic dynein heavy chains, and division of labor among the isoforms would provide a mechanism to regulate dynein function. The targeted disruption of somatic genes in Tetrahymena thermophila presents the opportunity to determine the contributions of individual dynein isoforms in a single cell that expresses multiple dynein heavy chain genes. Substantial portions of two Tetrahymena cytoplasmic dynein heavy chain genes were cloned, and their motor domains were sequenced. Tetrahymena DYH1 encodes the ubiquitous cytoplasmic dynein Dyh1, and DYH2 encodes a second cytoplasmic dynein isoform, Dyh2. The disruption of DYH1, but not DYH2, resulted in cells with two detectable defects: 1) phagocytic activity was inhibited, and 2) the cells failed to distribute their chromosomes correctly during micronuclear mitosis. In contrast, the disruption of DYH2 resulted in a loss of regulation of cell size and cell shape and in the apparent inability of the cells to repair their cortical cytoskeletons. We conclude that the two dyneins perform separate tasks in Tetrahymena.

The Tail of a Yeast Class V Myosin, Myo2p, Functions as a Localization Domain

Myo2p is a yeast class V myosin that functions in membrane trafficking. To investigate the function of the carboxyl-terminal-tail domain of Myo2p, we have overexpressed this domain behind the regulatable GAL1 promoter (MYO2DN). Overexpression of the tail domain of Myo2p results in a dominant–negative phenotype that is phenotypically similar to a temperature-sensitive allele of myo2, myo2–66. The tail domain of Myo2p is sufficient for localization at low- expression levels and causes mislocalization of the endogenous Myo2p from sites of polarized cell growth. Subcellular fractionation of polarized, mechanically lysed yeast cells reveals that Myo2p is present predominantly in a 100,000 × g pellet. The Myo2p in this pellet is not solubilized by Mg++-ATP or Triton X-100, but is solubilized by high salt. Tail overexpression does not disrupt this fractionation pattern, nor do mutations in sec4, sec3, sec9, cdc42, or myo2. These results show that overexpression of the tail domain of Myo2p does not compete with the endogenous Myo2p for assembly into a pelletable structure, but does compete with the endogenous Myo2p for a factor that is necessary for localization to the bud tip.

The Conserved Core of a Human SIR2 Homologue Functions in Yeast Silencing

Silencing is a universal form of transcriptional regulation in which regions of the genome are reversibly inactivated by changes in chromatin structure. Sir2 (Silent Information Regulator) protein is unique among the silencing factors in Saccharomyces cerevisiae because it silences the rDNA as well as the silent mating-type loci and telomeres. Discovery of a gene family of Homologues of Sir Two (HSTs) in organisms from bacteria to humans suggests that SIR2’s silencing mechanism might be conserved. The Sir2 and Hst proteins share a core domain, which includes two diagnostic sequence motifs of unknown function as well as four cysteines of a putative zinc finger. We demonstrate by mutational analyses that the conserved core and each of its motifs are essential for Sir2p silencing. Chimeras between Sir2p and a human Sir2 homologue (hSir2Ap) indicate that this human protein’s core can substitute for that of Sir2p, implicating the core as a silencing domain. Immunofluorescence studies reveal partially disrupted localization, accounting for the yeast–human chimeras’ ability to function at only a subset of Sir2p’s target loci. Together, these results support a model for the involvement of distinct Sir2p-containing complexes in HM/telomeric and rDNA silencing and that HST family members, including the widely expressed hSir2A, may perform evolutionarily conserved functions.

The Schizosaccharomyces pombe hst4+ Gene Is a SIR2 Homologue with Silencing and Centromeric Functions

Although silencing is a significant form of transcriptional regulation, the functional and mechanistic limits of its conservation have not yet been established. We have identified the Schizosaccharomyces pombe hst4+ gene as a member of the SIR2/HST silencing gene family that is defined in organisms ranging from bacteria to humans. hst4Δ mutants grow more slowly than wild-type cells and have abnormal morphology and fragmented DNA. Mutant strains show decreased silencing of reporter genes at both telomeres and centromeres. hst4+ appears to be important for centromere function as well because mutants have elevated chromosome-loss rates and are sensitive to a microtubule-destabilizing drug. Consistent with a role in chromatin structure, Hst4p localizes to the nucleus and appears concentrated in the nucleolus. hst4Δ mutant phenotypes, including growth and silencing phenotypes, are similar to those of the Saccharomyces cerevisiae HSTs, and at a molecular level, hst4+ is most similar to HST4. Furthermore, hst4+ is a functional homologue of S. cerevisiae HST3 and HST4 in that overexpression of hst4+ rescues the temperature-sensitivity and telomeric silencing defects of an hst3Δ hst4Δ double mutant. These results together demonstrate that a SIR-like silencing mechanism is conserved in the distantly related yeasts and is likely to be found in other organisms from prokaryotes to mammals.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Parsing executive processes: Strategic vs. evaluative functions of the anterior cingulate cortex

Event-related functional MRI and a version of the Stroop color naming task were used to test two conflicting theories of anterior cingulate cortex (ACC) function during executive processes of cognition. A response-related increase in ACC activity was present when strategic processes were less engaged, and conflict high, but not when strategic processes were engaged and conflict reduced. This is inconsistent with the widely held view that the ACC implements strategic processes to reduce cognitive conflicts, such as response competition. Instead, it suggests that the ACC serves an evaluative function, detecting cognitive states such as response competition, which may lead to poor performance, and representing the knowledge that strategic processes need to be engaged.

A new pathway for the secretion of virulence factors by bacteria: The flagellar export apparatus functions as a protein-secretion system

Biogenesis of the flagellum, a motive organelle of many bacterial species, is best understood for members of the Enterobacteriaceae. The flagellum is a heterooligomeric structure that protrudes from the surface of the cell. Its assembly initially involves the synthesis of a dedicated protein export apparatus that subsequently transports other flagellar proteins by a type III mechanism from the cytoplasm to the outer surface of the cell, where oligomerization occurs. In this study, the flagellum export apparatus was shown to function also as a secretion system for the transport of several extracellular proteins in the pathogenic bacterium Yersinia enterocolitica. One of the proteins exported by the flagellar secretion system was the virulence-associated phospholipase, YplA. These results suggest type III protein secretion by the flagellar system may be a general mechanism for the transport of proteins that influence bacterial–host interactions.

Borrelia burgdorferi periplasmic flagella have both skeletal and motility functions

Bacterial shape usually is dictated by the peptidoglycan layer of the cell wall. In this paper, we show that the morphology of the Lyme disease spirochete Borrelia burgdorferi is the result of a complex interaction between the cell cylinder and the internal periplasmic flagella. B. burgdorferi has a bundle of 7–11 helically shaped periplasmic flagella attached at each end of the cell cylinder and has a flat-wave cell morphology. Backward moving, propagating waves enable these bacteria to swim in both low viscosity media and highly viscous gel-like media. Using targeted mutagenesis, we inactivated the gene encoding the major periplasmic flagellar filament protein FlaB. The resulting flaB mutants not only were nonmotile, but were rod-shaped. Western blot analysis indicated that FlaB was no longer synthesized, and electron microscopy revealed that the mutants were completely deficient in periplasmic flagella. Wild-type cells poisoned with the protonophore carbonyl cyanide-m-chlorophenylhydrazone retained their flat-wave morphology, indicating that the periplasmic flagella do not need to be energized for the cell to maintain this shape. Our results indicate that the periplasmic flagella of B. burgdorferi have a skeletal function. These organelles dynamically interact with the rod-shaped cell cylinder to enable the cell to swim, and to confer in part its flat-wave morphology.

Parkin functions as an E2-dependent ubiquitin– protein ligase and promotes the degradation of the synaptic vesicle-associated protein, CDCrel-1

Parkinson's disease is a common neurodegenerative disorder in which familial-linked genes have provided novel insights into the pathogenesis of this disorder. Mutations in Parkin, a ring-finger-containing protein of unknown function, are implicated in the pathogenesis of autosomal recessive familial Parkinson's disease. Here, we show that Parkin binds to the E2 ubiquitin-conjugating human enzyme 8 (UbcH8) through its C-terminal ring-finger. Parkin has ubiquitin–protein ligase activity in the presence of UbcH8. Parkin also ubiquitinates itself and promotes its own degradation. We also identify and show that the synaptic vesicle-associated protein, CDCrel-1, interacts with Parkin through its ring-finger domains. Furthermore, Parkin ubiquitinates and promotes the degradation of CDCrel-1. Familial-linked mutations disrupt the ubiquitin–protein ligase function of Parkin and impair Parkin and CDCrel-1 degradation. These results suggest that Parkin functions as an E3 ubiquitin–protein ligase through its ring domains and that it may control protein levels via ubiquitination. The loss of Parkin's ubiquitin–protein ligase function in familial-linked mutations suggests that this may be the cause of familial autosomal recessive Parkinson's disease.

MLL, a mammalian trithorax-group gene, functions as a transcriptional maintenance factor in morphogenesis

Determinative events in vertebrate embryogenesis appear to require the continuous expression of spatial regulators such as the clustered homeobox genes. The mechanisms that govern long-term patterns of gene expression are not well understood. In Drosophila, active and silent states of developmentally regulated loci are maintained by trithorax and Polycomb group. We have examined the developmental role of a mammalian homolog of trx and putative oncogene, Mll. Knockout mice reveal that Mll is required for maintenance of gene expression early in embryogenesis. Downstream targets of Mll including Hoxa7 are activated appropriately in the absence of Mll but require Mll for sustaining their expression. The Mll−/− phenotype manifests later in development and is characterized by branchial arch dysplasia and aberrant segmental boundaries of spinal ganglia and somites. Thus, Mll represents an essential mechanism of transcriptional maintenance in mammalian development, which functions in multiple morphogenetic processes.

The PTEN/MMAC1 tumor suppressor phosphatase functions as a negative regulator of the phosphoinositide 3-kinase/Akt pathway

The PTEN/MMAC1 phosphatase is a tumor suppressor gene implicated in a wide range of human cancers. Here we provide biochemical and functional evidence that PTEN/MMAC1 acts a negative regulator of the phosphoinositide 3-kinase (PI3-kinase)/Akt pathway. PTEN/MMAC1 impairs activation of endogenous Akt in cells and inhibits phosphorylation of 4E-BP1, a downstream target of the PI3-kinase/Akt pathway involved in protein translation, whereas a catalytically inactive, dominant negative PTEN/MMAC1 mutant enhances 4E-BP1 phosphorylation. In addition, PTEN/MMAC1 represses gene expression in a manner that is rescued by Akt but not PI3-kinase. Finally, higher levels of Akt activation are observed in human prostate cancer cell lines and xenografts lacking PTEN/MMAC1 expression when compared with PTEN/MMAC1-positive prostate tumors or normal prostate tissue. Because constitutive activation of either PI3-kinase or Akt is known to induce cellular transformation, an increase in the activation of this pathway caused by mutations in PTEN/MMAC1 provides a potential mechanism for its tumor suppressor function.