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.
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Notes
Other than assuming uniform mixing, the thermodynamic properties of the molecules in the test tube (pot) are not included in the description of the assembly process. Also, a relatively uniform melting temperature for all sticky-ends is assumed.
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Acknowledgments
Authors would like to thank Stephen W. Suen, David A. Rabson, and the referees for providing valuable suggestions. The work is supported in part by NSF grants CCF #0726396 and CCF #0523928.
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Jonoska, N., McColm, G.L. & Staninska, A. On stoichiometry for the assembly of flexible tile DNA complexes. Nat Comput 10, 1121–1141 (2011). https://doi.org/10.1007/s11047-009-9169-1
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DOI: https://doi.org/10.1007/s11047-009-9169-1