Interval probe graphs and sandwich problems

Abstract

Physical mapping of DNA The use of interval models in molecular biology dates back to the original studies on the linearity of genes by the well-known biologist Seymore Benzer. In Benzer (1959), interval graphs were defined in order to study overlap data on sub-elements inside the gene. The question at that time was whether the overlap data was consistent with the hypothesis that genes are linear structures with the sub-elements being intervals on that line. If perfect and complete data were to be available for of all pairs of these sub-elements, then the problem would be that of recognizing an interval graph. However, with only partial data, as is always the case in experimental genetics, the problems involve embedding the data in a larger consistent set (e.g., interval graph completion). This will generally require inferring additional intersections (e.g., selectively adding chords to a cycle), and using additional biological information or assumptions to test consistency and propose the possible linear orderings. During the ensuing years, research in genetics has involved many combinatorial problems on intervals. One of these is DNA physical mapping, in which one wishes to find the linear order of segments (physically contiguous units) of the chromosome. It is an essential part of most sequencing, gene locating, and cloning projects. One of the main goals set for the Human Genome Project is to obtain a detailed mapping of all human chromosomes.