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Topological questions related to DNA self-assembly of graph structures
by
Natasha Jonoska
Department of Mathematics, University of South Florida
Coauthors: Masahico Saito
Recent years have seen the advent of DNA-based computatioin as well as development of DNA nanotechnology. All these are based mainly on DNA self-assembly of three dimensional objects, robust devices and periodic arrays. Main building blocks in these assemblies are branched junction molecules. Arbitrary non-regular graphs can also be constructed by using junction molecules as vertices and duplex DNA molecules as edge connectors. Many NP-complete problems such as 3-SAT can be solved by graph self-assembply in one biostep (one-pot reaction). There are several mathematical problems that arise from these assemblies such as the minimal number of DNA strands needed for construction of the graph. We address this question by considering the DNA strands that make up the graphh as boundaries of a compact orientable surface (2-dimensional manifold) such that the graph is topologically embedded (as 1-complex) as deformation retract. We will also discuss DNA splicing and present a topological model for studying splicing processes.
Date received: October 1, 2004
Copyright © 2004 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # capf-04.