We have identified three new members of the olfactory receptor (OR) gene family within a large segment of DNA that is duplicated with high similarity near many human telomeres. This segment is present at 3q, 15q, and 19p in each of 45 unrelated humans sampled from various populations. Additional copies are present polymorphically at 11 other subtelomeric locations. The frequency with which the block is present at some locations varies among populations. While humans carry seven to 11 copies of the OR-containing block, it is located in chimpanzee and gorilla predominantly at a single site, which is not orthologous to any of the locations in the human genome. The observation that sequences flanking the OR-containing segment are duplicated on larger and different sets of chromosomes than the OR block itself demonstrates that the segment is part of a much larger, complex patchwork of subtelomeric duplications. The population analyses and structural results suggest the types of processes that have shaped these regions during evolution. From its sequence, one of the OR genes in this duplicated block appears to be potentially functional. Our findings raise the possibility that functional diversity in the OR family is generated in part through duplications and inter-chromosomal rearrangements of the DNA near human telomeres.

The three-dimensional structures of two isozymes of manganese peroxidase (MnP) have been predicted from homology modeling using lignin peroxidase as a template. Although highly homologous, MnP differs from LiP by the requirement of Mn(II) as an intermediate in its oxidation of substrates. The Mn(II) site is absent in LiP and unique to the MnP family of peroxidases. The model structures were used to identify the unique Mn(II) binding sites, to determine to what extent they were conserved in the two isozymes, and to provide insight into why this site is absent in LiP. For each isozyme of MnP, three candidate Mn(II) binding sites were identified. Energy optimizations of the three possible Mn(II) enzyme complexes allowed the selection of the most favorable Mn(II) binding site as one with the most anionic oxygen moieties best configured to act as ligands for the Mn(II). At the preferred site, the Mn(II) is coordinated to the carboxyl oxygens of Glu-35, Glu-39, and Asp-179, and a propionate group of the heme. The predicted Mn(II) binding site is conserved in both isozymes. Comparison between the residues at this site in MnP and the corresponding residues in LiP shows that two of the three anionic residues in MnP are replaced by neutral residues in LiP, explaining why LiP does not bind Mn(II).

A second-order direct trajectory optimization method in which the state time history is described by Chebychev polynomials and the dynamical equations are satisfied by penalty functions is described. The convergence and fidelity of the method are demonstrated with solutions to the following problems: brachistochrone, subsonic transport minimum-time climb, supersonic interceptor minimum-time climb, Goddard rocket problem with a singular arc, subsonic transport minimum-fuel for a fixed-range mission including climb, cruise and descent, and optimal evasive maneuvers for an airplane pursued by a missile with proportional guidance. The results demonstrate that the method provides an efficient and reliable procedure for solving a wide variety of realistic trajectory optimization problems.