Advances in random matrix theory, zeta functions, and sphere packing

Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues (“the energy levels”) follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks.

Prime factors

We use Voiculescu’s free probability theory to prove the existence of prime factors, hence answering a longstanding problem in the theory of von Neumann algebras.

Numbers and Organization of RNA Polymerases, Nascent Transcripts, and Transcription Units in HeLa Nuclei

Using HeLa cells, we have developed methods to determine 1) the number of RNA polymerases that are active at any moment, 2) the number of transcription sites, and 3) the number of polymerases associated with one transcription unit. To count engaged polymerases, cells were encapsulated in agarose, permeabilized, treated with ribonuclease, and the now-truncated transcripts extended in [32P]uridine triphosphate; then, the number of growing transcripts was calculated from the total number of nucleotides incorporated and the average increment in length of the transcripts. Approximately 15,000 transcripts were elongated by polymerase I, and ∼75,000 were elongated by polymerases II and III. Transcription sites were detected after the cells were grown in bromouridine for <2.5 min, after which the resulting bromo-RNA was labeled with gold particles; electron microscopy showed that most extranucleolar transcripts were concentrated in ∼2400 sites with diameters of ∼80 nm. The number of polymerases associated with a transcription unit was counted after templates were spread over a large area; most extranucleolar units were associated with one elongating complex. These results suggest that many templates are attached in a “cloud” of loops around a site; each site, or transcription “factory,” would contain ∼30 active polymerases and associated transcripts.

IL-4 and -5 prime human mast cells for different profiles of IgE-dependent cytokine production

Mast cells (MC) are stem cell factor-dependent tissue-based hematopoietic cells with substantial functional heterogeneity. Cord blood-derived human MC (hMC) express functional receptors for IL-5, and IL-5 mediates stem cell factor-dependent comitogenesis of hMC in vitro. Although IL-5 is not required for normal hMC development, we considered that it might prime hMC for their high-affinity Fc receptor for IgE (FcɛRI)-dependent generation of cytokines, as previously demonstrated for IL-4. Compared with hMC maintained in stem cell factor alone, hMC primed with IL-5 expressed 2- to 4-fold higher steady-state levels of TNF-α, IL-5, IL-13, macrophage inflammatory protein 1α, and granulocyte-macrophage colony-stimulating factor transcripts 2 h after FcɛRI crosslinking and secreted 2- to 5-fold greater quantities of the corresponding cytokines, except IL-13, at 6 h. Unlike IL-4, IL-5 priming did not enhance FcɛRI-dependent histamine release. Thus, IL-5 augments cytokine production by hMC by a mechanism distinct from that of IL-4 and with a different resultant profile of cytokine production. These observations suggest a potentially autocrine effect of IL-5 on hMC for amplification of allergic immune responses, in addition to its recognized paracrine effects on eosinophils, and implicate both IL-4 and IL-5 in the modulation of the hMC phenotype.

Virus-specific CD8+ T cell numbers are maintained during γ-herpesvirus reactivation in CD4-deficient mice

The murine γ-herpesvirus 68 replicates in epithelial sites after intranasal challenge, then persists in various cell types, including B lymphocytes. Mice that lack CD4+ T cells (I-Ab−/−) control the acute infection, but suffer an ultimately lethal recrudescence of lytic viral replication in the respiratory tract. The consequences of CD4+ T cell deficiency for the generation and maintenance of murine γ-herpesvirus 68-specific CD8+ set now have been analyzed by direct staining with viral peptides bound to major histocompatibility complex class I tetramers and by a spectrum of functional assays. Both acutely and during viral reactivation, the CD8+ T cell responses in the I-Ab−/− group were no less substantial than in the I-Ab+/+ controls. Indeed, virus-specific CD8+ T cell numbers were increased in the lymphoid tissue of clinically compromised I-Ab−/− mice, although relatively few of the potential cytotoxic T lymphocyte effectors were recruited back to the site of pathology in the lung. Thus the viral reactivation that occurs in the absence of CD4+ T cells was not associated with any exhaustion of the virus-specific cytotoxic T lymphocyte response. It seems that CD8+ T cells alone are insufficient to maintain long-term control of this persistent γ-herpesvirus.

Numbers of deaths related to intrapartum asphyxia and timing of birth in all Wales perinatal survey, 1993-5

Objectives: To investigate the relation between the timing of birth and the occurrence of death related to an intrapartum event.

Mendel-GFDb and Mendel-ESTS: databases of plant gene families and ESTs annotated with gene family numbers and gene family names

There is no control over the information provided with sequences when they are deposited in the sequence databases. Consequently mistakes can seed the incorrect annotation of other sequences. Grouping genes into families and applying controlled annotation overcomes the problems of incorrect annotation associated with individual sequences. Two databases (http://www.mendel.ac.uk) were created to apply controlled annotation to plant genes and plant ESTs: Mendel-GFDb is a database of plant protein (gene) families based on gapped-BLAST analysis of all sequences in the SWISS-PROT family of databases. Sequences are aligned (ClustalW) and identical and similar residues shaded. The families are visually curated to ensure that one or more criteria, for example overall relatedness and/or domain similarity relate all sequences within a family. Sequence families are assigned a ‘Gene Family Number’ and a unified description is developed which best describes the family and its members. If authority exists the gene family is assigned a ‘Gene Family Name’. This information is placed in Mendel-GFDb. Mendel-ESTS is primarily a database of plant ESTs, which have been compared to Mendel-GFDb, completely sequenced genomes and domain databases. This approach associated ESTs with individual sequences and the controlled annotation of gene families and protein domains; the information being placed in Mendel-ESTS. The controlled annotation applied to genes and ESTs provides a basis from which a plant transcription database can be developed.