Characteristic enrichment of DNA repeats in different genomes

Using computer programs developed for this purpose, we searched for various repeated sequences including inverted, direct tandem, and homopurine–homopyrimidine mirror repeats in various prokaryotes, eukaryotes, and an archaebacterium. Comparison of observed frequencies with expectations revealed that in bacterial genomes and organelles the frequency of different repeats is either random or enriched for inverted and/or direct tandem repeats. By contrast, in all eukaryotic genomes studied, we observed an overrepresentation of all repeats, especially homopurine–homopyrimidine mirror repeats. Analysis of the genomic distribution of all abundant repeats showed that they are virtually excluded from coding sequences. Unexpectedly, the frequencies of abundant repeats normalized for their expectations were almost perfect exponential functions of their size, and for a given repeat this function was indistinguishable between different genomes.

A high-resolution annotated physical map of the human chromosome 13q12-13 region containing the breast cancer susceptibility locus BRCA2.

Various types of physical mapping data were assembled by developing a set of computer programs (Integrated Mapping Package) to derive a detailed, annotated map of a 4-Mb region of human chromosome 13 that includes the BRCA2 locus. The final assembly consists of a yeast artificial chromosome (YAC) contig with 42 members spanning the 13q12-13 region and aligned contigs of 399 cosmids established by cross-hybridization between the cosmids, which were selected from a chromosome 13-specific cosmid library using inter-Alu PCR probes from the YACs. The end sequences of 60 cosmids spaced nearly evenly across the map were used to generate sequence-tagged sites (STSs), which were mapped to the YACs by PCR. A contig framework was generated by STS content mapping, and the map was assembled on this scaffold. Additional annotation was provided by 72 expressed sequences and 10 genetic markers that were positioned on the map by hybridization to cosmids.

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.

Folding funnels and frustration in off-lattice minimalist protein landscapes

A full quantitative understanding of the protein folding problem is now becoming possible with the help of the energy landscape theory and the protein folding funnel concept. Good folding sequences have a landscape that resembles a rough funnel where the energy bias towards the native state is larger than its ruggedness. Such a landscape leads not only to fast folding and stable native conformations but, more importantly, to sequences that are robust to variations in the protein environment and to sequence mutations. In this paper, an off-lattice model of sequences that fold into a β-barrel native structure is used to describe a framework that can quantitatively distinguish good and bad folders. The two sequences analyzed have the same native structure, but one of them is minimally frustrated whereas the other one exhibits a high degree of frustration.

Progress toward chemical accuracy in the computer simulation of condensed phase reactions.

We describe a procedure for the generation of chemically accurate computer-simulation models to study chemical reactions in the condensed phase. The process involves (i) the use of a coupled semiempirical quantum and classical molecular mechanics method to represent solutes and solvent, respectively; (ii) the optimization of semiempirical quantum mechanics (QM) parameters to produce a computationally efficient and chemically accurate QM model; (iii) the calibration of a quantum/classical microsolvation model using ab initio quantum theory; and (iv) the use of statistical mechanical principles and methods to simulate, on massively parallel computers, the thermodynamic properties of chemical reactions in aqueous solution. The utility of this process is demonstrated by the calculation of the enthalpy of reaction in vacuum and free energy change in aqueous solution for a proton transfer involving methanol, methoxide, imidazole, and imidazolium, which are functional groups involved with proton transfers in many biochemical systems. An optimized semiempirical QM model is produced, which results in the calculation of heats of formation of the above chemical species to within 1.0 kcal/mol (1 kcal = 4.18 kJ) of experimental values. The use of the calibrated QM and microsolvation QM/MM (molecular mechanics) models for the simulation of a proton transfer in aqueous solution gives a calculated free energy that is within 1.0 kcal/mol (12.2 calculated vs. 12.8 experimental) of a value estimated from experimental pKa values of the reacting species.