On stoichiometry for the assembly of flexible tile DNA complexes

Authors:
N. Jonoska;G. L. Mccolm;A. Staninska
Affiliations:
Department of Mathematics & Statistics, University of South Florida, Tampa, USA 33620;Department of Mathematics & Statistics, University of South Florida, Tampa, USA 33620;Institute of Biomathematics and Biometry Helmholtz Zentrum München, Neuherberg, Germany 85764
Venue:
Natural Computing: an international journal
Year:
2011

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Abstract

Given a set of flexible branched junction DNA molecules with sticky-ends (building blocks), called here "tiles", we consider the problem of determining the proper stoichiometry such that all sticky-ends could end up connected. In general, the stoichiometry is not uniform, and the goal is to determine the proper proportion (spectrum) of each type of molecule within a test tube to allow for complete assembly. According to possible components that assemble in complete complexes we partition multisets of tiles, called here "pots", into classes: unsatisfiable, weakly satisfiable, satisfiable and strongly satisfiable. This classification is characterized through the spectrum of the pot, and it can be computed in PTIME using the standard Gauss-Jordan elimination method. We also give a geometric description of the spectrum as a convex hull within the unit cube.