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.

Pronounced and sustained central hypernoradrenergic function in major depression with melancholic features: Relation to hypercortisolism and corticotropin-releasing hormone

Both stress-system activation and melancholic depression are characterized by fear, constricted affect, stereotyped thinking, and similar changes in autonomic and neuroendocrine function. Because norepinephrine (NE) and corticotropin-releasing hormone (CRH) can produce these physiological and behavioral changes, we measured the cerebrospinal fluid (CSF) levels each hour for 30 consecutive hours in controls and in patients with melancholic depression. Plasma adrenocorticotropic hormone (ACTH) and cortisol levels were obtained every 30 min. Depressed patients had significantly higher CSF NE and plasma cortisol levels that were increased around the clock. Diurnal variations in CSF NE and plasma cortisol levels were virtually superimposable and positively correlated with each other in both patients and controls. Despite their hypercortisolism, depressed patients had normal levels of plasma ACTH and CSF CRH. However, plasma ACTH and CSF CRH levels in depressed patients were inappropriately high, considering the degree of their hypercortisolism. In contrast to the significant negative correlation between plasma cortisol and CSF CRH levels seen in controls, patients with depression showed no statistical relationship between these parameters. These data indicate that persistent stress-system dysfunction in melancholic depression is independent of the conscious stress of the disorder. These data also suggest mutually reinforcing bidirectional links between a central hypernoradrenergic state and the hyperfunctioning of specific central CRH pathways that each are driven and sustained by hypercortisolism. We postulate that α-noradrenergic blockade, CRH antagonists, and treatment with antiglucocorticoids may act at different loci, alone or in combination, in the treatment of major depression with melancholic features.

Gain- and loss-of-function of Rhp51, a Rad51 homolog in fission yeast, reveals dissimilarities in chromosome integrity

Rad51 is crucial not only in homologous recombination and recombinational repair but also in normal cellular growth. To address the role of Rad51 in normal cell growth we investigated morphological changes of cells after overexpression of wild-type and a dominant negative form of Rad51 in fission yeast. Rhp51, a Rad51 homolog in Schizosaccharomyces pombe, has a highly conserved ATP-binding motif. Rhp51 K155A, which has a single substitution in this motif, failed to rescue hypersensitivity of a rhp51Δ mutant to methyl methanesulfonate (MMS) and UV, whereas it binds normally to Rhp51 and Rad22, a Rad52 homolog. Two distinct cellular phenotypes were observed when Rhp51 or Rhp51 K155A was overexpressed in normal cells. Overexpression of Rhp51 caused lethality in the absence of DNA-damaging agents, with acquisition of a cell cycle mutant phenotype and accumulation of a 1C DNA population. On the other hand, overexpression of Rhp51 K155A led to a delay in G2 with decondensed nuclei, which resembled the phenotype of rhp51Δ. The latter also exhibited MMS and UV sensitivity, indicating that Rhp51 K155A has a dominant negative effect. These results suggest an association between DNA replication and Rad51 function.

Segregation of viral plasmids depends on tethering to chromosomes and is regulated by phosphorylation

Eukaryotic viruses can maintain latency in dividing cells as extrachromosomal nuclear plasmids. Segregation and nuclear retention of DNA is, therefore, a key issue in retaining copy number. The E2 enhancer protein of the papillomaviruses is required for viral DNA replication and transcription. Viral mutants that prevent phosphorylation of the bovine papillomavirus type 1 (BPV) E2 protein are transformation-defective, despite normal viral gene expression and replication function. Cell colonies harboring such mutants show sectoring of viral DNA and are unable to maintain the episome. We find that transforming viral DNA attaches to mitotic chromosomes, in contrast to the mutant genome encoding the E2 phosphorylation mutant. Second-site suppressor mutations were uncovered in both E1 and E2 genes that allow for transformation, maintenance, and chromosomal attachment. E2 protein was also found to colocalize to mitotic chromosomes, whereas the mutant did not, suggesting a direct role for E2 in viral attachment to chromosomes. Such viral hitch-hiking onto cellular chromosomes is likely to provide a general mechanism for maintaining nuclear plasmids.

Disease sequence from mutant rhodopsin allele to rod and cone photoreceptor degeneration in man

Mutations in the gene encoding rhodopsin, the visual pigment in rod photoreceptors, lead to retinal degeneration in species from Drosophila to man. The pathogenic sequence from rod cell-specific mutation to degeneration of rods and cones remains unclear. To understand the disease process in man, we studied heterozygotes with 18 different rhodopsin gene mutations by using noninvasive tests of rod and cone function and retinal histopathology. Two classes of disease expression were found, and there was allele-specificity. Class A mutants lead to severely abnormal rod function across the retina early in life; topography of residual cone function parallels cone cell density. Class B mutants are compatible with normal rods in adult life in some retinal regions or throughout the retina, and there is a slow stereotypical disease sequence. Disease manifests as a loss of rod photoreceptor outer segments, not singly but in microscopic patches that coalesce into larger irregular areas of degeneration. Cone outer segment function remains normal until >75% of rod outer segments are lost. The topography of cone loss coincides with that of rod loss. Most class B mutants show an inferior-nasal to superior-temporal retinal gradient of disease vulnerability associated with visual cycle abnormalities. Class A mutant alleles behave as if cytotoxic; class B mutants can be relatively innocuous and epigenetic factors may play a major role in the retinal degeneration.

Diversification, expression, and γδ T cell recognition of evolutionarily distant members of the MIC family of major histocompatibility complex class I-related molecules

Distant relatives of major histocompatibility complex (MHC) class I molecules, human MICA and MICB, function as stress-induced antigens that are broadly recognized by intestinal epithelial γδ T cells. They may thus play a central role in the immune surveillance of damaged, infected, or otherwise stressed intestinal epithelial cells. However, the generality of this system in evolution and the mode of recognition of MICA and MICB are undefined. Analysis of cDNA sequences from various primate species defined translation products that are homologous to MICA and MICB. All of the MIC polypeptides have common characteristics, although they are extraordinarily diverse. The most notable alterations are several deletions and frequent amino acid substitutions in the putative α-helical regions of the α1α2 domains. However, the primate MIC molecules were expressed on the surfaces of normal and transfected cells. Moreover, despite their sharing of relatively few identical amino acids in potentially accessible regions of their α1α2 domains, they were recognized by diverse human intestinal epithelial γδ T cells that are restricted by MICA and MICB. Thus, MIC molecules represent a family of MHC proteins that are structurally diverse yet appear to be functionally conserved. The promiscuous mode of γδ T cell recognition of these antigens may be explained by their sharing of a single conserved interaction site.

Design, synthesis, and biological characterization of a peptide-mimetic antagonist for a tethered-ligand receptor

Protease-activated receptors (PARs) represent a unique family of seven-transmembrane G protein-coupled receptors, which are enzymatically cleaved to expose a truncated extracellular N terminus that acts as a tethered activating ligand. PAR-1 is cleaved and activated by the serine protease α-thrombin, is expressed in various tissues (e.g., platelets and vascular cells), and is involved in cellular responses associated with hemostasis, proliferation, and tissue injury. We have discovered a series of potent peptide-mimetic antagonists of PAR-1, exemplified by RWJ-56110. Spatial relationships between important functional groups of the PAR-1 agonist peptide epitope SFLLRN were employed to design and synthesize candidate ligands with appropriate groups attached to a rigid molecular scaffold. Prototype RWJ-53052 was identified and optimized via solid-phase parallel synthesis of chemical libraries. RWJ-56110 emerged as a potent, selective PAR-1 antagonist, devoid of PAR-1 agonist and thrombin inhibitory activity. It binds to PAR-1, interferes with PAR-1 calcium mobilization and cellular function (platelet aggregation; cell proliferation), and has no effect on PAR-2, PAR-3, or PAR-4. By flow cytometry, RWJ-56110 was confirmed as a direct inhibitor of PAR-1 activation and internalization, without affecting N-terminal cleavage. At high concentrations of α-thrombin, RWJ-56110 fully blocked activation responses in human vascular cells, albeit not in human platelets; whereas, at high concentrations of SFLLRN-NH2, RWJ-56110 blocked activation responses in both cell types. Thus, thrombin activates human platelets independently of PAR-1, i.e., through PAR-4, which we confirmed by PCR analysis. Selective PAR-1 antagonists, such as RWJ-56110, should serve as useful tools to study PARs and may have therapeutic potential for treating thrombosis and restenosis.

Phalangeal curvature and positional behavior in extinct sloth lemurs (Primates, Palaeopropithecidae)

Recent paleontological discoveries in Madagascar document the existence of a diverse clade of palaeopropithecids or “sloth lemurs”: Mesopropithecus (three species), Babakotia (one species), Palaeopropithecus (three species), and Archaeoindris (one species). This mini-radiation of now extinct (“subfossil”) lemurs is most closely related to the living indrids (Indri, Propithecus, and Avahi). Whereas the extant indrids are known for their leaping acrobatics, the palaeopropithecids (except perhaps for the poorly known giant Archaeoindris) exhibit numerous skeletal design features for antipronograde or suspensory positional behaviors (e.g., high intermembral indices and mobile joints). Here we analyze the curvature of the proximal phalanges of the hands and feet. Computed as the included angle (θ), phalangeal curvature develops in response to mechanical use and is known to be correlated in primates with hand and foot function in different habitats; terrestrial species have straighter phalanges than their arboreal counterparts, and highly suspensory forms such as the orangutan possess the most curved phalanges. Sloth lemurs as a group are characterized by very curved proximal phalanges, exceeding those seen in spider monkeys and siamangs, and approaching that of orangutans. Indrids have curvatures roughly half that of sloth lemurs, and the more terrestrial, subfossil Archaeolemur possesses the least curved phalanges of all the indroids. Taken together with many other derived aspects of their postcranial anatomy, phalangeal curvature indicates that the sloth lemurs are one of the most suspensory clades of mammals ever to evolve.

Role of brain allopregnanolone in the plasticity of γ-aminobutyric acid type A receptor in rat brain during pregnancy and after delivery

The relation between changes in brain and plasma concentrations of neurosteroids and the function and structure of γ-aminobutyric acid type A (GABAA) receptors in the brain during pregnancy and after delivery was investigated in rats. In contrast with plasma, where all steroids increased in parallel, the kinetics of changes in the cerebrocortical concentrations of progesterone, allopregnanolone (AP), and allotetrahydrodeoxycorticosterone (THDOC) diverged during pregnancy. Progesterone was already maximally increased between days 10 and 15, whereas AP and allotetrahydrodeoxycorticosterone peaked around day 19. The stimulatory effect of muscimol on 36Cl− uptake by cerebrocortical membrane vesicles was decreased on days 15 and 19 of pregnancy and increased 2 days after delivery. Moreover, the expression in cerebral cortex and hippocampus of the mRNA encoding for γ2L GABAA receptor subunit decreased during pregnancy and had returned to control values 2 days after delivery. Also α1,α2, α3, α4, β1, β2, β3, and γ2S mRNAs were measured and failed to change during pregnancy. Subchronic administration of finasteride, a 5α-reductase inhibitor, to pregnant rats reduced the concentrations of AP more in brain than in plasma as well as prevented the decreases in both the stimulatory effect of muscimol on 36Cl− uptake and the decrease of γ2L mRNA observed during pregnancy. These results indicate that the plasticity of GABAA receptors during pregnancy and after delivery is functionally related to fluctuations in endogenous brain concentrations of AP whose rate of synthesis/metabolism appears to differ in the brain, compared with plasma, in pregnant rats.

Brca2 is coordinately regulated with Brca1 during proliferation and differentiation in mammary epithelial cells

We have analyzed the expression of the breast cancer susceptibility gene, Brca2, in mammary epithelial cells as a function of proliferation and differentiation. Our results demonstrate that Brca2 mRNA expression is tightly regulated during mammary epithelial proliferation and differentiation, and that this regulation occurs coordinately with Brca1. Specifically, Brca2 mRNA expression is up-regulated in rapidly proliferating cells; is down-regulated in response to serum deprivation; is expressed in a cell cycle-dependent manner, peaking at the G1/S boundary; and is up-regulated in differentiating mammary epithelial cells in response to glucocorticoids. In each case, an identical pattern of expression was observed for Brca1. These results indicate that proliferative stimuli modulate the mRNA expression of these two breast cancer susceptibility genes. In addition, the coordinate regulation of Brca1 and Brca2 revealed by these experiments suggests that these genes are induced by, and may function in, overlapping regulatory pathways involved in the control of cell proliferation and differentiation.

RNA-controlled polymorphism in the in vivo assembly of 180-subunit and 120-subunit virions from a single capsid protein

Repeated, specific interactions between capsid protein (CP) subunits direct virus capsid assembly and exemplify regulated protein–protein interactions. The results presented here reveal a striking in vivo switch in CP assembly. Using cryoelectron microscopy, three-dimensional image reconstruction, and molecular modeling, we show that brome mosaic virus (BMV) CP can assemble in vivo two remarkably distinct capsids that selectively package BMV-derived RNAs in the absence of BMV RNA replication: a 180-subunit capsid indistinguishable from virions produced in natural infections and a previously unobserved BMV capsid type with 120 subunits arranged as 60 CP dimers. Each such dimer contains two CPs in distinct, nonequivalent environments, in contrast to the quasi-equivalent CP environments throughout the 180-subunit capsid. This 120-subunit capsid utilizes most of the CP interactions of the 180-subunit capsid plus nonequivalent CP–CP interactions. Thus, the CP of BMV, and perhaps other viruses, can encode CP–CP interactions that are not apparent from mature virions and may function in assembly or disassembly. Shared structural features suggest that the 120- and 180-subunit capsids share assembly steps and that a common pentamer of CP dimers may be an important assembly intermediate. The ability of a single CP to switch between distinct capsids by means of alternate interactions also implies reduced evolutionary barriers between different capsid structures. The in vivo switch between alternate BMV capsids is controlled by the RNA packaged: a natural BMV genomic RNA was packaged in 180-subunit capsids, whereas an engineered mRNA containing only the BMV CP gene was packaged in 120-subunit capsids. RNA features can thus direct the assembly of a ribonucleoprotein complex between alternate structural pathways.

Localization of a putative transcriptional regulator (ATRX) at pericentromeric heterochromatin and the short arms of acrocentric chromosomes

ATRX is a member of the SNF2 family of helicase/ATPases that is thought to regulate gene expression via an effect on chromatin structure and/or function. Mutations in the hATRX gene cause severe syndromal mental retardation associated with α-thalassemia. Using indirect immunofluorescence and confocal microscopy we have shown that ATRX protein is associated with pericentromeric heterochromatin during interphase and mitosis. By coimmunofluorescence, ATRX localizes with a mouse homologue of the Drosophila heterochromatic protein HP1 in vivo, consistent with a previous two-hybrid screen identifying this interaction. From the analysis of a trap assay for nuclear proteins, we have shown that the localization of ATRX to heterochromatin is encoded by its N-terminal region, which contains a conserved plant homeodomain-like finger and a coiled-coil domain. In addition to its association with heterochromatin, at metaphase ATRX clearly binds to the short arms of human acrocentric chromosomes, where the arrays of ribosomal DNA are located. The unexpected association of a putative transcriptional regulator with highly repetitive DNA provides a potential explanation for the variability in phenotype of patients with identical mutations in the ATRX gene.

Cloning and characterization of a corepressor and potential component of the nuclear hormone receptor repression complex

Nuclear hormone receptors are potent repressors of transcription in the unliganded state. We describe here the cloning of a nuclear receptor corepressor that we call SUN-CoR (Small Unique Nuclear receptor CoRepressor), which shows no homology to previously described nuclear hormone receptor corepressors, N-CoR, or SMRT. SUN-CoR is a highly basic, 16-kDa nuclear protein that is expressed at high levels in adult tissues and is induced during adipocyte and myogenic differentiation. SUN-CoR potentiates transcriptional repression by thyroid hormone receptor and RevErb in vivo, represses transcription when fused to a heterologous DNA binding domain, and interacts with RevErb as well as with thyroid hormone receptor in vitro. SUN-CoR also interacts with N-CoR and SMRT in vitro and with endogenous N-CoR in cells. We conclude that SUN-CoR is a corepressor and may function as an additional component of the complex involved in transcriptional repression by unliganded and orphan nuclear hormone receptors.

Erp1p and Erp2p, Partners for Emp24p and Erv25p in a Yeast p24 Complex

Six new members of the yeast p24 family have been identified and characterized. These six genes, named ERP1–ERP6 (for Emp24p- and Erv25p-related proteins) are not essential, but deletion of ERP1 or ERP2 causes defects in the transport of Gas1p, in the retention of BiP, and deletion of ERP1 results in the suppression of a temperature-sensitive mutation in SEC13 encoding a COPII vesicle coat protein. These phenotypes are similar to those caused by deletion of EMP24 or ERV25, two previously identified genes that encode related p24 proteins. Genetic and biochemical studies demonstrate that Erp1p and Erp2p function in a heteromeric complex with Emp24p and Erv25p.

Activation of Androgen Receptor Function by a Novel Nuclear Protein Kinase

Androgen receptor (AR) belongs to the nuclear receptor superfamily and mediates the biological actions of male sex steroids. In this work, we have characterized a novel 130-kDa Ser/Thr protein kinase ANPK that interacts with the zinc finger region of AR in vivo and in vitro. The catalytic kinase domain of ANPK shares considerable sequence similarity with the minibrain gene product, a protein kinase suggested to contribute to learning defects associated with Down syndrome. However, the rest of ANPK sequence, including the AR-interacting interface, exhibits no apparent homology with other proteins. ANPK is a nuclear protein that is widely expressed in mammalian tissues. Its overexpression enhances AR-dependent transcription in various cell lines. In addition to the zinc finger region, ligand-binding domain and activation function AF1 of AR are needed, as the activity of AR mutants devoid of these domains was not influenced by ANPK. The receptor protein does not appear to be a substrate for ANPK in vitro, and overexpression of ANPK does not increase the extent of AR phosphorylation in vivo. In view of this, it is likely that ANPK-mediated activation of AR function is exerted through modification of AR-associated proteins, such as coregulatory factors, and/or through stabilization of the receptor protein against degradation.