Lower bounds on multiple sequence alignment using exact 3-way alignment

<p>Abstract</p> <p>Background</p> <p>Multiple sequence alignment is fundamental. Exponential growth in computation time appears to be inevitable when an optimal alignment is required for many sequences. Exact costs of optimum alignments are therefore rarely computed. Consequently much effort has been invested in algorithms for alignment that are heuristic, or explore a restricted class of solutions. These give an upper bound on the alignment cost, but it is equally important to determine the quality of the solution obtained. In the absence of an optimal alignment with which to compare, lower bounds may be calculated to assess the quality of the alignment. As more effort is invested in improving upper bounds (alignment algorithms), it is therefore important to improve lower bounds as well. Although numerous cost metrics can be used to determine the quality of an alignment, many are based on sum-of-pairs (SP) measures and their generalizations.</p> <p>Results</p> <p>Two standard and two new methods are considered for using exact 2-way and 3-way alignments to compute lower bounds on total SP alignment cost; one new method fares well with respect to accuracy, while the other reduces the computation time. The first employs exhaustive computation of exact 3-way alignments, while the second employs an efficient heuristic to compute a much smaller number of exact 3-way alignments. Calculating all 3-way alignments exactly and computing their average improves lower bounds on sum of SP cost in <it>v</it>-way alignments. However judicious selection of a subset of all 3-way alignments can yield a further improvement with minimal additional effort. On the other hand, a simple heuristic to select a random subset of 3-way alignments (a random packing) yields accuracy comparable to averaging all 3-way alignments with substantially less computational effort.</p> <p>Conclusion</p> <p>Calculation of lower bounds on SP cost (and thus the quality of an alignment) can be improved by employing a mixture of 3-way and 2-way alignments.</p

The epithelial cell rests of Malassez - a role in periodontal regeneration?

The definitive version is available at www.blackwell-synergy.comThis article reviews general aspects about the epithelial cell rests of Malassez (ERM). The historical and general morphological features of the ERM are briefly described. The embryological derivation of the ERM is presented as an important consideration in understanding the events associated with their origin and possible functional roles within the periodontal ligament. The ultrastructural description of the ERM is also included to complement the morphological characteristics which distinguish these cells as the unique epithelial element of the periodontal ligament. The unique ability of these cells to synthesize and secrete a number of proteins usually associated with cells of mesenchymal origin, rather than ectodermal origin, is discussed in light of their role in cementum repair and regeneration. Such considerations lead to our hypothesis that one of the functional roles of the ERM may lie not only their role in maintaining and contributing to the normal periodontal cellular elements and function but also contributing, in a significant manner, to periodontal regeneration.J. C. Rincon, W. G. Young, P. M. Bartol