Abstract for the talk at 06.11.2007 (11:15 h)Arbeitsgemeinschaft MIKROSTRUKTUREN
The Spectrum of a pot with DNA molecules and related problems
A theoretical model of DNA self-assembly will be presented. For this model a problem is encoded in the molecules in a pot and a solution is represented by a complete complex (a complex that does not contain free sticky ends) of appropriate size. In most experiments, besides complete complexes, a lot of undesired material (non-complete complexes) also appears. To optimize the initial solution so as to minimize the amount of non-complete complexes at the end one needs to use proper proportion of molecule types. The set of vectors representing these proper proportions is called the ``spectrum" of the pot. The spectrum is a convex hull with rational vertices. The extreme points of this convex hull help us to determine some of the minimal complete complexes that could appear in the pot. Also, the spectrum help us to classify the pots. I will present some already proved facts for the spectrum as well as problems that I am currently working on.