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.

Resected RNA pseudoknots and their recognition by histidyl-tRNA synthetase

Duplexes constituted by closed or open RNA circles paired to single-stranded oligonucleotides terminating with 3′-CCAOH form resected pseudoknots that are substrates of yeast histidyl-tRNA synthetase. Design of this RNA fold is linked to the mimicry of the pseudoknotted amino acid accepting branch of the tRNA-like domain from brome mosaic virus, known to be charged by tyrosyl-tRNA synthetases, with RNA minihelices recapitulating accepting branches of canonical tRNAs. Prediction of the histidylation function of the new family of minimalist tRNA-like structures relates to the geometry of resected pseudoknots that allows proper presentation to histidyl-tRNA synthetase of analogues of the histidine identity determinants N-1 and N73 present in tRNAs. This geometry is such that the analogue of the major N-1 histidine determinant in the RNA circles faces the analogue of the discriminator N73 nucleotide in the accepting oligonucleotides. The combination of identity elements found in tRNAHis species from archaea, eubacteria, and organelles (G-1/C73) is the most efficient for determining histidylation of the duplexes. The inverse combination (C-1/G73) leads to the worst histidine acceptors with charging efficiencies reduced by 2–3 orders of magnitude. Altogether, these findings open new perspectives for understanding evolution of tRNA identity and serendipitous RNA functions.

Transcriptional adaptor and histone acetyltransferase proteins in Arabidopsis and their interactions with CBF1, a transcriptional activator involved in cold-regulated gene expression

The Arabidopsis CBF transcriptional activators bind to the CRT/DRE regulatory element present in the promoters of many cold-regulated genes and stimulate their transcription. Expression of the CBF1 proteins in yeast activates reporter genes carrying a minimal promoter with the CRT/DRE as an upstream regulatory element. Here we report that this ability of CBF1 is dependent upon the activities of three key components of the yeast Ada and SAGA complexes, namely the histone acetyltransferase (HAT) Gcn5 and the transcriptional adaptor proteins Ada2 and Ada3. This result suggested that CBF1 might function through the action of similar complexes in Arabidopsis. In support of this hypothesis we found that Arabidopsis has a homolog of the GCN5 gene and two homologs of ADA2, the first report of multiple ADA2 genes in an organism. The Arabidopsis GCN5 protein has intrinsic HAT activity and can physically interact in vitro with both the Arabidopsis ADA2a and ADA2b proteins. In addition, the CBF1 transcriptional activator can interact with the Arabidopsis GCN5 and ADA2 proteins. We conclude that Arabidopsis encodes HAT-containing adaptor complexes that are related to the Ada and SAGA complexes of yeast and propose that the CBF1 transcriptional activator functions through the action of one or more of these complexes.

The chaperone/usher pathways of Pseudomonas aeruginosa: Identification of fimbrial gene clusters (cup) and their involvement in biofilm formation

Pseudomonas aeruginosa, an important opportunistic human pathogen, persists in certain tissues in the form of specialized bacterial communities, referred to as biofilm. The biofilm is formed through series of interactions between cells and adherence to surfaces, resulting in an organized structure. By screening a library of Tn5 insertions in a nonpiliated P. aeruginosa strain, we identified genes involved in early stages of biofilm formation. One class of mutations identified in this study mapped in a cluster of genes specifying the components of a chaperone/usher pathway that is involved in assembly of fimbrial subunits in other microorganisms. These genes, not previously described in P. aeruginosa, were named cupA1–A5. Additional chaperone/usher systems (CupB and CupC) have been also identified in the genome of P. aeruginosa PAO1; however, they do not appear to play a role in adhesion under the conditions where the CupA system is expressed and functions in surface adherence. The identification of these putative adhesins on the cell surface of P. aeruginosa suggests that this organism possess a wide range of factors that function in biofilm formation. These structures appear to be differentially regulated and may function at distinct stages of biofilm formation, or in specific environments colonized by this organism.

Two recombination-dependent DNA replication pathways of bacteriophage T4, and their roles in mutagenesis and horizontal gene transfer

Two major pathways of recombination-dependent DNA replication, “join-copy” and “join-cut-copy,” can be distinguished in phage T4: join-copy requires only early and middle genes, but two late proteins, endonuclease VII and terminase, are uniquely important in the join-cut-copy pathway. In wild-type T4, timing of these pathways is integrated with the developmental program and related to transcription and packaging of DNA. In primase mutants, which are defective in origin-dependent lagging-strand DNA synthesis, the late pathway can bypass the lack of primers for lagging-strand DNA synthesis. The exquisitely regulated synthesis of endo VII, and of two proteins from its gene, explains the delay of recombination-dependent DNA replication in primase (as well as topoisomerase) mutants, and the temperature-dependence of the delay. Other proteins (e.g., the single-stranded DNA binding protein and the products of genes 46 and 47) are important in all recombination pathways, but they interact differently with other proteins in different pathways. These homologous recombination pathways contribute to evolution because they facilitate acquisition of any foreign DNA with limited sequence homology during horizontal gene transfer, without requiring transposition or site-specific recombination functions. Partial heteroduplex repair can generate what appears to be multiple mutations from a single recombinational intermediate. The resulting sequence divergence generates barriers to formation of viable recombinants. The multiple sequence changes can also lead to erroneous estimates in phylogenetic analyses.