Cellular and molecular changes of the periodontium associated with a higher prevalence of oral diseases (e.g., chronic periodontitis) in aged populations have received little attention. Since impaired apoptosis during aging appears to be related to chronic inflammatory disorders, we hypothesized that the expression of genes associated with apoptotic processes are altered in aged healthy and periodontitis-affected gingival tissue.

In this review we discuss the computational and technical challenges associated with these studies, the approaches that have been developed to address these challenges and the advantages of cross-species analysis of microarray data. We show how successful application of these methods lead to insights that cannot be obtained when analyzing data from a single species. We also highlight current open problems and discuss possible ways to address them.

The popular neighbor-joining (NJ) algorithm used in phylogenetics is a greedy algorithm for finding the balanced minimum evolution (BME) tree associated to a dissimilarity map. From this point of view, NJ is "optimal" when the algorithm outputs the tree which minimizes the balanced minimum evolution criterion. We use the fact that the NJ tree topology and the BME tree topology are determined by polyhedral subdivisions of the spaces of dissimilarity maps to study the optimality of the neighbor-joining algorithm. In particular, we investigate and compare the polyhedral subdivisions for n ≤ 8. This requires the measurement of volumes of spherical polytopes in high dimension, which we obtain using a combination of Monte Carlo methods and polyhedral algorithms. Our results include a demonstration that highly unrelated trees can be co-optimal in BME reconstruction, and that NJ regions are not convex. We obtain the l 2 radius for neighborjoining for n = 5 and we conjecture that the ability of the neighbor-joining algorithm to recover the BME tree depends on the diameter of the BME tree.

Supplementary data are available at Bioinformatics online.