Parametrizations of elliptic curves by Shimura curves and by classical modular curves

Fix an isogeny class

SMART, a simple modular architecture research tool: Identification of signaling domains

Accurate multiple alignments of 86 domains that occur in signaling proteins have been constructed and used to provide a Web-based tool (SMART: simple modular architecture research tool) that allows rapid identification and annotation of signaling domain sequences. The majority of signaling proteins are multidomain in character with a considerable variety of domain combinations known. Comparison with established databases showed that 25% of our domain set could not be deduced from SwissProt and 41% could not be annotated by Pfam. SMART is able to determine the modular architectures of single sequences or genomes; application to the entire yeast genome revealed that at least 6.7% of its genes contain one or more signaling domains, approximately 350 greater than previously annotated. The process of constructing SMART predicted (i) novel domain homologues in unexpected locations such as band 4.1-homologous domains in focal adhesion kinases; (ii) previously unknown domain families, including a citron-homology domain; (iii) putative functions of domain families after identification of additional family members, for example, a ubiquitin-binding role for ubiquitin-associated domains (UBA); (iv) cellular roles for proteins, such predicted DEATH domains in netrin receptors further implicating these molecules in axonal guidance; (v) signaling domains in known disease genes such as SPRY domains in both marenostrin/pyrin and Midline 1; (vi) domains in unexpected phylogenetic contexts such as diacylglycerol kinase homologues in yeast and bacteria; and (vii) likely protein misclassifications exemplified by a predicted pleckstrin homology domain in a Candida albicans protein, previously described as an integrin.

Adjoint modular Galois representations and their Selmer groups

In the last 15 years, many class number formulas and main conjectures have been proven. Here, we discuss such formulas on the Selmer groups of the three-dimensional adjoint representation ad(φ) of a two-dimensional modular Galois representation φ. We start with the p-adic Galois representation φ0 of a modular elliptic curve E and present a formula expressing in terms of L(1, ad(φ0)) the intersection number of the elliptic curve E and the complementary abelian variety inside the Jacobian of the modular curve. Then we explain how one can deduce a formula for the order of the Selmer group Sel(ad(φ0)) from the proof of Wiles of the Shimura–Taniyama conjecture. After that, we generalize the formula in an Iwasawa theoretic setting of one and two variables. Here the first variable, T, is the weight variable of the universal p-ordinary Hecke algebra, and the second variable is the cyclotomic variable S. In the one-variable case, we let φ denote the p-ordinary Galois representation with values in GL2(Zp[[T]]) lifting φ0, and the characteristic power series of the Selmer group Sel(ad(φ)) is given by a p-adic L-function interpolating L(1, ad(φk)) for weight k + 2 specialization φk of φ. In the two-variable case, we state a main conjecture on the characteristic power series in Zp[[T, S]] of Sel(ad(φ) ⊗ ν−1), where ν is the universal cyclotomic character with values in Zp[[S]]. Finally, we describe our recent results toward the proof of the conjecture and a possible strategy of proving the main conjecture using p-adic Siegel modular forms.

Congruences between modular forms: Raising the level and dropping Euler factors

We discuss the relationship among certain generalizations of results of Hida, Ribet, and Wiles on congruences between modular forms. Hida’s result accounts for congruences in terms of the value of an L-function, and Ribet’s result is related to the behavior of the period that appears there. Wiles’ theory leads to a class number formula relating the value of the L-function to the size of a Galois cohomology group. The behavior of the period is used to deduce that a formula at “nonminimal level” is obtained from one at “minimal level” by dropping Euler factors from the L-function.

Modular organization of intrinsic connections associated with spectral tuning in cat auditory cortex

Many response properties in primary auditory cortex (AI) are segregated spatially and organized topographically as those in primary visual cortex. Intensive study has not revealed an intrinsic, anatomical organizing principle related to an AI functional topography. We used retrograde anatomic tracing and topographic physiologic mapping of acoustic response properties to reveal long-range (≥1.5 mm) convergent intrinsic horizontal connections between AI subregions with similar bandwidth and characteristic frequency selectivity. This suggests a modular organization for processing spectral bandwidth in AI.

Modular construction for function of a ribonucleoprotein enzyme: the catalytic domain of Bacillus subtilis RNase P complexed with B.subtilis RNase P protein

The bacterial RNase P holoenzyme catalyzes the formation of the mature 5′-end of tRNAs and is composed of an RNA and a protein subunit. Among the two folding domains of the RNase P RNA, the catalytic domain (C-domain) contains the active site of this ribozyme. We investigated specific binding of the Bacillus subtilis C-domain with the B.subtilis RNase P protein and examined the catalytic activity of this C-domain–P protein complex. The C-domain forms a specific complex with the P protein with a binding constant of ∼0.1 µM. The C-domain–P protein complex and the holoenzyme are equally efficient in cleaving single-stranded RNA (∼0.9 min–1 at pH 7.8) and substrates with a hairpin–loop 3′ to the cleavage site (∼40 min–1). The holoenzyme reaction is much more efficient with a pre-tRNA substrate, binding at least 100-fold better and cleaving 10–500 times more efficiently. These results demonstrate that the RNase P holoenzyme is functionally constructed in three parts. The catalytic domain alone contains the active site, but has little specificity and affinity for most substrates. The specificity and affinity for the substrate is generated by either the specificity domain of RNase P RNA binding to a T stem–loop-like hairpin or RNase P protein binding to a single-stranded RNA. This modular construction may be exploited to obtain RNase P-based ribonucleoprotein complexes with altered substrate specificity.

A modular misexpression screen in Drosophila detecting tissue-specific phenotypes.

Genetic screens in Drosophila have lead to the discovery of many genes important for patterning and signal transduction in diverse organisms. Traditionally, the phenotypic effects of loss-of-function mutations are analyzed. As an alternative way to link genes and function, I have developed a versatile misexpression screen in Drosophila, the first such screen in higher eukaryotes. The screen identifies genes that, when over- or misexpressed in a pattern of interest, give a specific phenotype or modulate an existing mutant phenotype. It is based on Gal4 transactivation of a mobile enhancer and promoter that "targets" random endogenous genes for expression. The modular design of the screen allows directed expression in any temporal or spatial pattern. When activated in the developing eye, 4% of target inserts gave dominant phenotypes. One insertion was in the gene encoding Ras GTPase-activating protein; its overexpression phenotype was strongly enhanced by a mutation in Ras1. Thus, biologically relevant phenotypes and genetic interactions are identified using this method. The screen is a powerful new tool for developmental genetics; similar approaches can also be developed for other organisms.

Rescue of abasic hammerhead ribozymes by exogenous addition of specific bases.

We have synthesized 13 hammerhead ribozyme variants, each containing an abasic residue at a specific position of the catalytic core. The activity of each of the variants is significantly reduced. In four cases, however, activity can be rescued by exogenous addition of the missing base. For one variant, the rescue is 300-fold; for another, the rescue is to the wild-type level. This latter abasic variant (G10.1X) has been characterized in detail. Activation is specific for guanine, the base initially removed. In addition, the specificity for guanine versus adenine is substantially altered by replacing C with U in the opposite strand of the ribozyme. These results show that a binding site for a small, noncharged ligand can be created in a preexisting ribozyme structure. This has implications for structure-function analysis of RNA, and leads to speculations about evolution in an "RNA world" and about the potential therapeutic use of ribozymes.

Modular cis-regulatory organization of developmentally expressed genes: two genes transcribed territorially in the sea urchin embryo, and additional examples.

The cis-regulatory systems that control developmental expression of two sea urchin genes have been subjected to detailed functional analysis. Both systems are modular in organization: specific, separable fragments of the cis-regulatory DNA each containing multiple transcription factor target sites execute particular regulatory subfunctions when associated with reporter genes and introduced into the embryo. The studies summarized here were carried out on the CyIIIa gene, expressed in the embryonic aboral ectoderm and on the Endo16 gene, expressed in the embryonic vegetal plate, archenteron, and then midgut. The regulatory systems of both genes include modules that control particular aspects of temporal and spatial expression, and in both the territorial boundaries of expression depend on a combination of negative and positive functions. In both genes different regulatory modules control early and late embryonic expression. Modular cis-regulatory organization is widespread in developmentally regulated genes, and we present a tabular summary that includes many examples from mouse and Drosophila. We regard cis-regulatory modules as units of developmental transcription control, and also of evolution, in the assembly of transcription control systems.

COOH-terminal processing of nascent polypeptides by the glycosylphosphatidylinositol transamidase in the presence of hydrazine is governed by the same parameters as glycosylphosphatidylinositol addition.

Proteins anchored to the cell membrane via a glycosylphosphatidylinositol (GPI) moiety are found in all eukaryotes. After NH2-terminal peptide cleavage of the nascent protein by the signal peptidase, a second COOH-terminal signal peptide is cleaved with the concomitant addition of the GPI unit. The proposed mechanism of the GPI transfer is a transamidation reaction that involves the formation of an activated carbonyl intermediate (enzyme-substrate complex) with the ethanolamine moiety of the preassembled GPI unit serving as a nucleophile. Other nucleophilic acceptors like hydrazine (HDZ) and hydroxylamine have been shown to be possible alternate substrates for GPI. Since GPI has yet to be purified, the use of readily available nucleophilic substitutes such as HDZ and hydroxylamine is a viable alternative to study COOH-terminal processing by the putative transamidase. As a first step in developing a soluble system to study this process, we have examined the amino acid requirements at the COOH terminus for the transamidation reaction using HDZ as the nucleophilic acceptor instead of GPI. The hydrazide-forming reaction shows identical amino acid requirement profiles to that of GPI anchor addition. Additionally, we have studied other parameters relating to the kinetics of the transamidation reaction in the context of rough microsomal membranes. The findings with HDZ provide further evidence for the transamidase nature of the enzyme and also provide a starting point for development of a soluble assay.

Recruitment and replacement of hippocampal neurons in young and adult chickadees: an addition to the theory of hippocampal learning.

We used [3H]thymidine to document the birth of neurons and their recruitment into the hippocampal complex (HC) of juvenile (4.5 months old) and adult blackcapped chickadees (Parus atricapillus) living in their natural surroundings. Birds received a single dose of [3H]thymidine in August and were recaptured and killed 6 weeks later, in early October. All brains were stained with Cresyl violet, a Nissl stain. The boundaries of the HC were defined by reference to the ventricular wall, the brain surface, or differences in neuronal packing density. The HC of juveniles was as large as or larger than that of adults and packing density of HC neurons was 31% higher in juveniles than in adults. Almost all of the 3H-labeled HC neurons were found in a 350-m-wide layer of tissue adjacent to the lateral ventricle. Within this layer the fraction of 3H-labeled neurons was 50% higher in juveniles than in adults. We conclude that the HC of juvenile chickadees recruits more neurons and has more neurons than that of adults. We speculate that juveniles encounter greater environmental novelty than adults and that the greater number of HC neurons found in juveniles allows them to learn more than adults. At a more general level, we suggest that (i) long-term learning alters HC neurons irreversibly; (ii) sustained hippocampal learning requires the periodic replacement of HC neurons; (iii) memories coded by hippocampal neurons are transferred elsewhere before the neurons are replaced.

Yeast synaptobrevin homologs are modified posttranslationally by the addition of palmitate.

Yeast possess two homologs of the synaptobrevin family of vesicle-associated membrane proteins that function in membrane recognition and vesicle fusion. Yeast proteins Snc1 and Snc2 localize to secretory vesicles and are required for constitutive exocytosis. They also form a physical complex with a plasma membrane protein, Sec9, which is necessary for vesicle docking and fusion to occur in vivo. Formation of this molecular complex, as a prerequisite for vesicle fusion, appears to have been conserved evolutionarily. Here we demonstrate that Snc proteins undergo a single posttranslational modification with the addition of a palmitate moiety to Cys-95 in Snc1. Modification of Cys-95 (which is located proximal to the transmembrane domain) is rapid, occurs in the endoplasmic reticulum, and is long-lasting. Mutation of Cys-95 to Ser-95 blocks palmitoylation and appears to affect Snc protein stability. This provides evidence that synaptobrevin-like proteins are modified posttranslationally, and we predict that fatty acylation may be common to those found in higher eukaryotes.