Chloroplast protein and centrosomal genes, a tRNA intron, and odd telomeres in an unusually compact eukaryotic genome, the cryptomonad nucleomorph

Cells of several major algal groups are evolutionary chimeras of two radically different eukaryotic cells. Most of these “cells within cells” lost the nucleus of the former algal endosymbiont. But after hundreds of millions of years cryptomonads still retain the nucleus of their former red algal endosymbiont as a tiny relict organelle, the nucleomorph, which has three minute linear chromosomes, but their function and the nature of their ends have been unclear. We report extensive cryptomonad nucleomorph sequences (68.5 kb), from one end of each of the three chromosomes of Guillardia theta. Telomeres of the nucleomorph chromosomes differ dramatically from those of other eukaryotes, being repeats of the 23-mer sequence (AG)7AAG6A, not a typical hexamer (commonly TTAGGG). The subterminal regions comprising the rRNA cistrons and one protein-coding gene are exactly repeated at all three chromosome ends. Gene density (one per 0.8 kb) is the highest for any cellular genome. None of the 38 protein-coding genes has spliceosomal introns, in marked contrast to the chlorarachniophyte nucleomorph. Most identified nucleomorph genes are for gene expression or protein degradation; histone, tubulin, and putatively centrosomal ranbpm genes are probably important for chromosome segregation. No genes for primary or secondary metabolism have been found. Two of the three tRNA genes have introns, one in a hitherto undescribed location. Intergenic regions are exceptionally short; three genes transcribed by two different RNA polymerases overlap their neighbors. The reported sequences encode two essential chloroplast proteins, FtsZ and rubredoxin, thus explaining why cryptomonad nucleomorphs persist.

Even-odd alternation in mass spectrum of thymine and uracil clusters: Evidence of intracluster photodimerization

Multiphoton ionization of thymine and uracil clusters generated by a supersonic molecular beam gave rise to a remarkable alternation of mass spectral intensities between even- and odd-numbered clusters. Such alternation was observed in clusters of up to 30 molecules. Excitation to the two lowest electronically excited states seemed to be a strong prerequisite. In view of the well known photodimerization reaction of thymine and uracil in the bulk phase, it is proposed that such alternation in the mass spectral intensity resulted from formation of photodimer units within the cluster on intense UV irradiation. Several analogues of thymine with no known propensity for photodimerization in the bulk phase did not exhibit any sign of such alternation in the cluster mass spectrum. The intrinsic UV window for photodimerization, and hence photoinduced mammalian mutagenesis, was estimated to be approximately 210–280 nm, significantly narrower than the previously reported bulk values of 150–300 nm.

Linkage disequilibrium mapping in isolated populations: The example of Finland revisited

Linkage disequilibrium analysis can provide high resolution in the mapping of disease genes because it incorporates information on recombinations that have occurred during the entire period from the mutational event to the present. A circumstance particularly favorable for high-resolution mapping is when a single founding mutation segregates in an isolated population. We review here the population structure of Finland in which a small founder population some 100 generations ago has expanded into 5.1 million people today. Among the 30-odd autosomal recessive disorders that are more prevalent in Finland than elsewhere, several appear to have segregated for this entire period in the “panmictic” southern Finnish population. Linkage disequilibrium analysis has allowed precise mapping and determination of genetic distances at the 0.1-cM level in several of these disorders. Estimates of genetic distance have proven accurate, but previous calculations of the confidence intervals were too small because sampling variation was ignored. In the north and east of Finland the population can be viewed as having been “founded” only after 1500. Disease mutations that have undergone such a founding bottleneck only 20 or so generations ago exhibit linkage disequilibrium and haplotype sharing over long genetic distances (5–15 cM). These features have been successfully exploited in the mapping and cloning of many genes. We review the statistical issues of fine mapping by linkage disequilibrium and suggest that improved methodologies may be necessary to map diseases of complex etiology that may have arisen from multiple founding mutations.

Xenopus Zic3, a primary regulator both in neural and neural crest development

Xenopus Zic3 is a Xenopus homologue of mouse Zic and Drosophila pair-rule gene, odd-paired. We show here that Zic3 has significant roles both in neural and neural crest development in Xenopus embryo. Expression of Zic3 is first detected in prospective neural plate region at gastrulation. Onset of the expression was earlier than most proneural genes and followed chordin expression. The expression was induced by blockade of BMP4 signal. Overexpression of Zic3 resulted in hyperplastic neural and neural crest derived tissue. In animal cap explant, the overexpression of Zic3 induced expression of all the proneural genes and neural crest marker genes. These findings suggest that Zic3 can determine the ectodermal cell fate and promote the earliest step of neural and neural crest development.

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.

Zic2 regulates the kinetics of neurulation

Mutation in human ZIC2, a zinc finger protein homologous to Drosophila odd-paired, causes holoprosencephaly (HPE), which is a common, severe malformation of the brain in humans. However, the pathogenesis is largely unknown. Here we show that reduced expression (knockdown) of mouse Zic2 causes neurulation delay, resulting in HPE and spina bifida. Differentiation of the most dorsal neural plate, which gives rise to both roof plate and neural crest cells, also was delayed as indicated by the expression lag of a roof plate marker, Wnt3a. In addition the development of neural crest derivatives such as dorsal root ganglion was impaired. These results suggest that the Zic2 expression level is crucial for the timing of neurulation. Because the Zic2 knockdown mouse is the first mutant with HPE and spina bifida to survive to the perinatal period, the mouse will promote analyses of not only the neurulation but also the pathogenesis of human HPE.

Highly conserved features of DNA binding between two divergent members of the Myb family of transcription factors

Bas1p, a divergent yeast member of the Myb family of transcription factors, shares with the proteins of this family a highly conserved cysteine residue proposed to play a role in redox regulation. Substitutions of this residue in Bas1p (C153) allowed us to establish that, despite its very high conservation, it is not strictly required for Bas1p function: its substitution with a small hydrophobic residue led to a fully functional protein in vitro and in vivo. C153 was accessible to an alkylating agent in the free protein but was protected by prior exposure to DNA. The reactivity of cysteines in the first and third repeats was much lower than in the second repeat, suggesting a more accessible conformation of repeat 2. Proteolysis protection, fluorescence quenching and circular dichroism experiments further indicated that DNA binding induces structural changes making Bas1p less accessible to modifying agents. Altogether, our results strongly suggest that the second repeat of the DNA-binding domain of Bas1p behaves similarly to its Myb counterpart, i.e. a DNA-induced conformational change in the second repeat leads to formation of a full helix–turn–helix-related motif with the cysteine packed in the hydrophobic core of the repeat.

Methylenetetrahydrofolate reductase (MTHFR) polymorphisms and risk of molecularly defined subtypes of childhood acute leukemia

Low folate intake as well as alterations in folate metabolism as a result of polymorphisms in the enzyme methylenetetrahydrofolate reductase (MTHFR) have been associated with an increased incidence of neural tube defects, vascular disease, and some cancers. Polymorphic variants of MTHFR lead to enhanced thymidine pools and better quality DNA synthesis that could afford some protection from the development of leukemias, particularly those with translocations. We now report associations of MTHFR polymorphisms in three subgroups of pediatric leukemias: infant lymphoblastic or myeloblastic leukemias with MLL rearrangements and childhood lymphoblastic leukemias with either TEL-AML1 fusions or hyperdiploid karyotypes. Pediatric leukemia patients (n = 253 total) and healthy newborn controls (n = 200) were genotyped for MTHFR polymorphisms at nucleotides 677 (C→T) and 1,298 (A→C). A significant association for carriers of C677T was demonstrated for leukemias with MLL translocations (MLL+, n = 37) when compared with controls [adjusted odd ratios (OR) = 0.36 with a 95% confidence interval (CI) of 0.15–0.85; P = 0.017]. This protective effect was not evident for A1298C alleles (OR = 1.14). In contrast, associations for A1298C homozygotes (CC; OR = 0.26 with a 95% CI of 0.07–0.81) and C677T homozygotes (TT; OR = 0.49 with a 95% CI of 0.20–1.17) were observed for hyperdiploid leukemias (n = 138). No significant associations were evident for either polymorphism with TEL-AML1+ leukemias (n = 78). These differences in allelic associations may point to discrete attributes of the two alleles in their ability to alter folate and one-carbon metabolite pools and impact after DNA synthesis and methylation pathways, but should be viewed cautiously pending larger follow-up studies. The data provide evidence that molecularly defined subgroups of pediatric leukemias have different etiologies and also suggest a role of folate in the development of childhood leukemia.

On degree 2 Galois representations over

We discuss proofs of some new special cases of Serre’s conjecture on odd, degree 2 representations of Gℚ.

Nucellain, a Barley Homolog of the Dicot Vacuolar-Processing Protease, Is Localized in Nucellar Cell Walls1

The nucellus is a complex maternal grain tissue that embeds and feeds the developing cereal endosperm and embryo. Differential screening of a barley (Hordeum vulgare) cDNA library from 5-d-old ovaries resulted in the isolation of two cDNA clones encoding nucellus-specific homologs of the vacuolar-processing enzyme of castor bean (Ricinus communis). Based on the sequence of these barley clones, which are called nucellains, a homolog from developing corn (Zea mays) grains was also identified. In dicots the vacuolar-processing enzyme is believed to be involved in the processing of vacuolar storage proteins. RNA-blot and in situ-hybridization analyses detected nucellain transcripts in autolysing nucellus parenchyma cells, in the nucellar projection, and in the nucellar epidermis. No nucellain transcripts were detected in the highly vacuolate endosperm or in the other maternal tissues of developing grains such as the testa or the pericarp. Using an antibody raised against castor bean vacuolar-processing protease, a single polypeptide was recognized in protein extracts from barley grains. Immunogold-labeling experiments with this antibody localized the nucellain epitope not in the vacuoles, but in the cell walls of all nucellar cell types. We propose that nucellain plays a role in processing and/or turnover of cell wall proteins in developing cereal grains.

Ergodic theorems along sequences and Hardy fields.

Let a(x) be a real function with a regular growth as x --> infinity. [The precise technical assumption is that a(x) belongs to a Hardy field.] We establish sufficient growth conditions on a(x) so that the sequence ([a(n)])(infinity)(n=1) is a good averaging sequence in L2 for the pointwise ergodic theorem. A sequence (an) of positive integers is a good averaging sequence in L2 for the pointwise ergodic theorem if in any dynamical system (Omega, Sigma, m, T) for f [symbol, see text] in L2(Omega) the averages [equation, see text] converge for almost every omicron in. Our result implies that sequences like ([ndelta]), where delta > 1 and not an integer, ([n log n]), and ([n2/log n]) are good averaging sequences for L2. In fact, all the sequences we examine will turn out to be good averaging for Lp, p > 1; and even for L log L. We will also establish necessary and sufficient growth conditions on a(x) so that the sequence ([a(n)]) is good averaging for mean convergence. Note that for some a(x) (e.g., a(x) = log2 x), ([a(n)]) may be good for mean convergence without being good for pointwise convergence.

Distribution of spontaneous plant hybrids.

Natural hybridization is a relatively common feature of vascular plant species and has been demonstrated to have played an important role in their evolution. Nonetheless, it is not clear whether spontaneous hybridization occurs as a general feature of all plant families and genera or whether certain groups are especially prone to spontaneous hybridization. Therefore, we inspected five modern biosystematic floras to survey the frequency and taxonomic distribution of spontaneous hybrids. We found spontaneous hybridization to be nonrandomly distributed among taxa, concentrated in certain families and certain genera, often at a frequency out of proportion to the size of the family or genus. Most of these groups were primarily outcrossing perennials with reproductive modes that stabilized hybridity such as agamospermy, vegetative spread, or permanent odd polyploidy. These data suggest that certain phylogenetic groups are biologically predisposed for the formation and maintenance of hybrids.