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.

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.

Brittle-1, an Adenylate Translocator, Facilitates Transfer of Extraplastidial Synthesized ADP-Glucose into Amyloplasts of Maize Endosperms1

Amyloplasts of starchy tissues such as those of maize (Zea mays L.) function in the synthesis and accumulation of starch during kernel development. ADP-glucose pyrophosphorylase (AGPase) is known to be located in chloroplasts, and for many years it was generally accepted that AGPase was also localized in amyloplasts of starchy tissues. Recent aqueous fractionation of young maize endosperm led to the conclusion that 95% of the cellular AGPase was extraplastidial, but immunolocalization studies at the electron- and light-microscopic levels supported the conclusion that maize endosperm AGPase was localized in the amyloplasts. We report the results of two nonaqueous procedures that provide evidence that in maize endosperms in the linear phase of starch accumulation, 90% or more of the cellular AGPase is extraplastidial. We also provide evidence that the brittle-1 protein (BT1), an adenylate translocator with a KTGGL motif common to the ADP-glucose-binding site of starch synthases and bacterial glycogen synthases, functions in the transfer of ADP-glucose into the amyloplast stroma. The importance of the BT1 translocator in starch accumulation in maize endosperms is demonstrated by the severely reduced starch content in bt1 mutant kernels.

An isolated, surface-expressed I domain of the integrin αLβ2 is sufficient for strong adhesive function when locked in the open conformation with a disulfide bond

We introduced disulfide bonds to lock the integrin αLβ2 I domain in predicted open, ligand binding or closed, nonbinding conformations. Transfectants expressing αLβ2 heterodimers containing locked-open but not locked-closed or wild-type I domains constitutively adhered to intercellular adhesion molecule-1 (ICAM-1) substrates. Locking the I domain closed abolished constitutive and activatable adhesion. The isolated locked-open I domain bound as well as the activated αLβ2 heterodimer, and binding was abolished by reduction of the disulfide. Lovastatin, which binds under the conformationally mobile C-terminal α-helix of the I domain, inhibited binding to ICAM-1 by αLβ2 with wild-type, but not locked-open I domains. These data establish the importance of conformational change in the αL I domain for adhesive function and show that this domain is sufficient for full adhesive activity.

Manipulation of the membrane binding site of vitamin K-dependent proteins: Enhanced biological function of human factor VII

Recent studies suggested that modification of the membrane contact site of vitamin K-dependent proteins may enhance the membrane affinity and function of members of this protein family. The properties of a factor VII mutant, factor VII-Q10E32, relative to wild-type factor VII (VII, containing P10K32), have been compared. Membrane affinity of VII-Q10E32 was about 20-fold higher than that of wild-type factor VII. The rate of autoactivation VII-Q10E32 with soluble tissue factor was 100-fold faster than wild-type VII and its rate of activation by factor Xa was 30 times greater than that of wild-type factor VII. When combined with soluble tissue factor and phospholipid, activated factor VII-Q10E32 displayed increased activation of factor X. Its coagulant activity was enhanced in all types of plasma and with all sources of tissue factor tested. This difference in activity (maximum 50-fold) was greatest when coagulation conditions were minimal, such as limiting levels of tissue factor and/or phospholipid. Because of its enhanced activity, factor VII-Q10E32 and its derivatives may provide important reagents for research and may be more effective in treatment of bleeding and/or clotting disorders.

T1/ST2 is preferentially expressed on murine Th2 cells, independent of interleukin 4, interleukin 5, and interleukin 10, and important for Th2 effector function

T helper (Th) cells can be categorized according to their cytokine expression. The differential induction of Th cells expressing Th1 and/or Th2 cytokines is key to the regulation of both protective and pathological immune responses. Cytokines are expressed transiently and there is a lack of stably expressed surface molecules, significant for functionally different types of Th cells. Such molecules are of utmost importance for the analysis and selective functional modulation of Th subsets and will provide new therapeutic strategies for the treatment of allergic or autoimmune diseases. To this end, we have identified potential target genes preferentially expressed in Th2 cells, expressing interleukin (IL)-4, IL-5, and/or IL-10, but not interferon-γ. One such gene, T1/ST2, is expressed stably on both Th2 clones and Th2-polarized cells activated in vivo or in vitro. T1/ST2 expression is independent of induction by IL-4, IL-5, or IL-10. T1/ST2 plays a critical role in Th2 effector function. Administration of either a mAb against T1/ST2 or recombinant T1/ST2 fusion protein attenuates eosinophilic inflammation of the airways and suppresses IL-4 and IL-5 production in vivo following adoptive transfer of Th2 cells.

Mendel’s dwarfing gene: cDNAs from the Le alleles and function of the expressed proteins

The major gibberellin (GA) controlling stem elongation in pea (Pisum sativum L.) is GA1, which is formed from GA20 by 3β-hydroxylation. This step, which limits GA1 biosynthesis in pea, is controlled by the Le locus, one of the original Mendelian loci. Mutations in this locus result in dwarfism. We have isolated cDNAs encoding a GA 3β-hydroxylase from lines of pea carrying the Le, le, le-3, and led alleles. The cDNA sequences from le and le-3 each contain a base substitution resulting in single amino acid changes relative to the sequence from Le. The cDNA sequence from led, a mutant derived from an le line, contains both the le “mutation” and a single-base deletion, which causes a shift in reading frame and presumably a null mutation. cDNAs from each line were expressed in Escherichia coli. The expression product for the clone from Le converted GA9 to GA4, and GA20 to GA1, with Km values of 1.5 μM and 13 μM, respectively. The amino acid substitution in the clone from le increased Km for GA9 100-fold and reduced conversion of GA20 to almost nil. Expression products from le and le-3 possessed similar levels of 3β-hydroxylase activity, and the expression product from led was inactive. Our results suggest that the 3β-hydroxylase cDNA is encoded by Le. Le transcript is expressed in roots, shoots, and cotyledons of germinating pea seedlings, in internodes and leaves of established seedlings, and in developing seeds.

The lipid bilayer determines helical tilt angle and function in lactose permease of Escherichia coli

The structure of lactose permease from Escherichia coli in its lipid environment was studied by attenuated total reflection Fourier transform infrared spectroscopy. The protein exhibits an α-helical content of about 65% and about 25% β-sheet. Unusually fast hydrogen/deuterium (H/D) exchange to 90–95% completion suggests a structure that is highly accessible to the aqueous phase. An average tilt angle of 33° for the helices was found with respect to the bilayer normal at a lipid-to-protein ratio of ≈800:1 (mol/mol), and the permease exhibits optimal activity under these conditions. However, upon decreasing the lipid-to-protein ratio, activity decreases continuously in a manner that correlates with the decrease in the lipid order parameter and the increase in the average helical tilt angle. Taken together, the data indicate that the structure and function of the permease are strongly dependent on the order and integrity of the lipid bilayer.

Mouse Eya genes are expressed during limb tendon development and encode a transcriptional activation function

Vertebrate limb tendons are derived from connective cells of the lateral plate mesoderm. Some of the developmental steps leading to the formation of vertebrate limb tendons have been previously identified; however, the molecular mechanisms responsible for tendinous patterning and maintenance during embryogenesis are largely unknown. The eyes absent (eya) gene of Drosophila encodes a novel nuclear protein of unknown molecular function. Here we show that Eya1 and Eya2, two mouse homologues of Drosophila eya, are expressed initially during limb development in connective tissue precursor cells. Later in limb development, Eya1 and Eya2 expression is associated with cell condensations that form different sets of limb tendons. Eya1 expression is largely restricted to flexor tendons, while Eya2 is expressed in the extensor tendons and ligaments of the phalangeal elements of the limb. These data suggest that Eya genes participate in the patterning of the distal tendons of the limb. To investigate the molecular functions of the Eya gene products, we have analyzed whether the highly divergent PST (proline-serine-threonine)-rich N-terminal regions of Eya1–3 function as transactivation domains. Our results demonstrate that Eya gene products can act as transcriptional activators, and they support a role for this molecular function in connective tissue patterning.

INAF, a protein required for transient receptor potential Ca2+ channel function

The trp gene of Drosophila encodes a subunit of a class of Ca2+-selective light-activated channels that carry the bulk of the phototransduction current. Transient receptor potential (TRP) homologs have been identified throughout animal phylogeny. In vertebrates, TRP-related channels have been suggested to mediate “store-operated Ca2+ entry,” which is important in Ca2+ homeostasis in a wide variety of cell types. However, the mechanisms of activation and regulation of the TRP channel are not known. Here, we report on the Drosophila inaF gene, which encodes a highly eye-enriched protein, INAF, that appears to be required for TRP channel function. A null mutation in this gene significantly reduces the amount of the TRP protein and, in addition, specifically affects the TRP channel function so as to nearly shut down its activity. The inaF mutation also dramatically suppresses the severe degeneration caused by a constitutively active mutation in the trp gene. Although the reduction in the amount of the TRP protein may contribute to these phenotypes, several lines of evidence support the view that inaF mutations also more directly affect the TRP channel function, suggesting that the INAF protein may have a regulatory role in the channel function.

Functional analyses of troponin T mutations that cause hypertrophic cardiomyopathy: Insights into disease pathogenesis and troponin function

Mutations in a number of cardiac sarcomeric protein genes cause hypertrophic cardiomyopathy (HCM). Previous findings indicate that HCM-causing mutations associated with a truncated cardiac troponin T (TnT) and missense mutations in the β-myosin heavy chain share abnormalities in common, acting as dominant negative alleles that impair contractile performance. In contrast, Lin et al. [Lin, D., Bobkova, A., Homsher, E. & Tobacman, L. S. (1996) J. Clin. Invest. 97, 2842–2848] characterized a TnT point mutation (Ile79Asn) and concluded that it might lead to hypercontractility and, thus, potentially a different mechanism for HCM pathogenesis. In this study, three HCM-causing cardiac TnT mutations (Ile79Asn, Arg92Gln, and ΔGlu160) were studied in a myotube expression system. Functional studies of wild-type and mutant transfected myotubes revealed that all three mutants decreased the calcium sensitivity of force production and that the two missense mutations (Ile79Asn and Arg92Gln) increased the unloaded shortening velocity nearly 2-fold. The data demonstrate that TnT can alter the rate of myosin cross-bridge detachment, and thus the troponin complex plays a greater role in modulating muscle contractile performance than was recognized previously. Furthermore, these data suggest that these TnT mutations may cause disease via an increased energetic load on the heart. This would represent a second paradigm for HCM pathogenesis.

Cannabinoid CB1 receptors and ligands in vertebrate retina: Localization and function of an endogenous signaling system

CB1, a cannabinoid receptor enriched in neuronal tissue, was found in high concentration in retinas of rhesus monkey, mouse, rat, chick, goldfish, and tiger salamander by using a subtype-specific polyclonal antibody. Immunolabeling was detected in the two synaptic layers of the retina, the inner and outer plexiform layers, of all six species examined. In the outer plexiform layer, CB1 was located in and/or on cone pedicles and rod spherules. Labeling was detected in some amacrine cells of all species and in the ganglion cells and ganglion cell axons of all species except fish. In addition, sparse labeling was found in the inner and/or outer segments of the photoreceptors of monkey, mouse, rat, and chick. Using GC/MS to detect possible endogenous cannabinoids, we found 3 nmol of 2-arachidonylglycerol per g of tissue, but no anandamide was detectable. Cannabinoid receptor agonists induced a dramatic reduction in the amplitude of voltage-gated L-type calcium channel currents in identified retinal bipolar cells. The presence and distribution of the CB1 receptor, the large amounts of 2-arachidonylglycerol found, and the effects of cannabinoids on calcium channel activity in bipolar cells suggest a substantive role for an endogenous cannabinoid signaling system in retinal physiology, and perhaps vision in general.

A homeobox gene with potential developmental control function in the meristem of the conifer Picea abies

Many homeobox genes control essential developmental processes in animals and plants. In this report, we describe the first cDNA corresponding to a homeobox gene isolated from a gymnosperm, the HBK1 gene from the conifer Picea abies (L.) Karst (Norway spruce). The sequence shows distinct similarities specifically to the KNOX (knotted-like homeobox) class of homeobox genes known from different angiosperm plants. The deduced amino acid sequence of HBK1 is strikingly similar within the homeodomain (84% identical) to the maize gene Knotted1 (Kn1), which acts to regulate cell differentiation in the shoot meristem. This similarity suggested that the phylogenetic association of HBK1 with the KNOX genes might be coupled to a conservation of gene function. In support of this suggestion, we have found HBK1 to be expressed in the apical meristem in the central population of nondifferentiated stem cells, but not in organ primordia developing at the flanks of the meristem. This pattern of expression is similar to that of Kn1 in the maize meristem. We show further that HBK1, when expressed ectopically in transgenic Arabidopsis plants, causes aberrations in leaf development that are similar to the effects of ectopic expression of angiosperm KNOX genes on Arabidopsis development. Taken together, these data suggest that HBK1 has a role, similar to the KNOX genes in angiosperms, in the control of cellular differentiation in the apical meristem of spruce. The data also indicate that KNOX-gene regulation of vegetative development is an ancient feature of seed plants that was present in the last common ancestor of conifers and angiosperms.

The AMPA receptor subunit GluR-B in its Q/R site-unedited form is not essential for brain development and function

Calcium permeability of l-α-amino-3-hydroxy-5-methyl-4-isoxazolepropionate receptors (AMPARs) in excitatory neurons of the mammalian brain is prevented by coassembly of the GluR-B subunit, which carries an arginine (R) residue at a critical site of the channel pore. The codon for this arginine is created by site-selective adenosine deamination of an exonic glutamine (Q) codon at the pre-mRNA level. Thus, central neurons can potentially control the calcium permeability of AMPARs by the level of GluR-B gene expression as well as by the extent of Q/R-site editing, which in postnatal brain, positions the R codon into >99% of GluR-B mRNA. To study whether the small amount of unedited GluR-B is of functional relevance, we have generated mice carrying GluR-B alleles with an exonic arginine codon. We report that these mutants manifest no obvious deficiencies, indicating that AMPAR-mediated calcium influx into central neurons can be solely regulated by the levels of Q/R site-edited GluR-B relative to other AMPAR subunits. Notably, a targeted GluR-B gene mutant with 30% reduced GluR-B levels had 2-fold higher AMPAR-mediated calcium permeability in hippocampal pyramidal cells with no sign of cytotoxicity. This constitutes proof in vivo that elevated calcium influx through AMPARs need not generate pathophysiological consequences.