John M. Mercer

Some considerations on the calculation of the velocity correlation function in the ring approximation, with application to the Lorentz gas

Some new methods are discussed for the calculation of the velocity correlation function in the Ring approximation. Theory and computer “experiments” are compared, with reasonable success, for the case of the Lorentz gas.

Expansion of the Kinetic Hierarchy for a Massive Particle: The Repeated Ring and Fokker-Planck Equations

The tagged particle BBGKY hierarchy is systematically expanded in inverse powers of the square root of the particle mass. In the Brownian limit, for fixed Knudsen number, the hierarchy reduces to the Brownian limit of the repeated ring equation which itself reduces to the Fokker-Planck equation. The friction coefficient of the Fokker-Planck equation is found to be a functional of the solution of Dorfman, van Beijeren, and McClures extended Boltzmann equation for a fixed object in a flowing gas. As a consequence, the tagged particle diffusion coefficient calculated in the Brownian limit of the repeated ring equation is valid for all particle sizes.

RNase 1 genes from the family Sciuridae define a novel rodent ribonuclease cluster

The RNase A ribonucleases are a complex group of functionally diverse secretory proteins with conserved enzymatic activity. We have identified novel RNase 1 genes from four species of squirrel (order Rodentia, family Sciuridae). Squirrel RNase 1 genes encode typical RNase A ribonucleases, each with eight cysteines, a conserved CKXXNTF signature motif, and a canonical His12-Lys41-His119 catalytic triad. Two alleles encode Callosciurus prevostii RNase 1, which include a Ser18↔Pro, analogous to the sequence polymorphisms found among the RNase 1 duplications in the genome of Rattus exulans. Interestingly, although the squirrel RNase 1 genes are closely related to one another (77–95% amino acid sequence identity), the cluster as a whole is distinct and divergent from the clusters including RNase 1 genes from other rodent species. We examined the specific sites at which Sciuridae RNase 1s diverge from Muridae/Cricetidae RNase 1s and determined that the divergent sites are located on the external surface, with complete sparing of the catalytic crevice. The full significance of these findings awaits a more complete understanding of biological role of mammalian RNase 1s.

Further development of the approach of Peralta and Zwanzig. I. The drag on a sphere at high bath densities

A simple analytical calculation is given for the drag on a ’’center of force’’ in a fluid flowing at infinity, following the approach of Peralta and Zwanzig. For infinite ramp and step potentials, we reproduce their results with new techniques which greatly simplify the calculation. We discuss the reason why the method does not give Stokes’ law, and we present a reasonable approximate method which does give Stokes’ law.

Slip-sliding away: serial changes and homoplasy in repeat number in the Drosophila yakuba homolog of human cancer susceptibility gene BRCA2.

Several recent studies have examined the function and evolution of a Drosophila homolog to the human breast cancer susceptibility gene BRCA2, named dmbrca2. We previously identified what appeared to be a recent expansion in the RAD51-binding BRC-repeat array in the ancestor of Drosophila yakuba. In this study, we examine patterns of variation and evolution of the dmbrca2 BRC-repeat array within D. yakuba and its close relatives. We develop a model of how unequal crossing over may have produced the expanded form, but we also observe short repeat forms, typical of other species in the D. melanogaster group, segregating within D. yakuba and D. santomea. These short forms do not appear to be identical-by-descent, suggesting that the history of dmbrca2 in the D. melanogaster subgroup has involved repeat unit contractions resulting in homoplasious forms. We conclude that the evolutionary history of dmbrca2 in D. yakuba and perhaps in other Drosophila species may be more complicated than can be inferred from examination of the published single genome sequences per species.

Unequal Crossing Over

Unequal crossing-over (UCO) occurs when distinct loci similar in sequence undergo homologous recombination. UCO was inferred from a series of experiments on the Bar locus in Drosophila melanogaster , demonstrating that crossing-over occurred in conjunction with Bar locus mutations. The process may result in duplication and deletion of genetic material, formation of chimeric genes, and the generation of mobile extrachromosomal elements. Contemporary studies of newly abundant genomic data show multicellular genomes to be filled with gene families whose formation can best be understood through UCO. Primates have been found to have substantial copy number variation (CNV) generated through nonallelic homologous recombination (NAHR), a type of UCO that occurs among highly similar sequences. The genetic variation produced is substantial, exceeding even single-nucleotide polymorphisms (SNPs) on a per-base-pair basis. That variation has major genetic disease-generating capability but also provides new variation for evolutionary processes. UCO plays a central role in chromosomal rearrangements (inversions, translocations), gene duplication, and tandem duplication of functional and structural modules especially in multicellular organisms, generation of gene families, and generation of mobile genetic materials such as exons – all important sources of the genetic variation necessary for evolution.