Abstract
Using linear DNA segments and branched junction molecules many different three-dimensional DNA structures (graphs) could be self-assembled. We investigate maximum and minimum numbers of circular DNA that form these structures. For a given graph G, we consider compact orientable surfaces, called thickened graphs of G, that have G as a deformation retract. The number of boundary curves of a thickened graph G corresponds to the number of circular DNA strands that assemble into the graph G. We investigate how this number changes by recombinations or edge additions and relate to some results from topological graph theory.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. Archdeacon, Topological graph theory, a survey, Congressus Numerantium 115 (1996), 5–54.
G. Chartrand and L. Lesniak, Graphs and Digraphs, Third Edition, Chapman and Hall, London, 1996.
N.R. Cozzarelli, The structure and function of DNA supercoiling and catenanes, The Harvey Lecture Series, 87 (1993) 35–55.
N. Jonoska, S. Karl, and M. Saito, Creating 3-dimensional graph structures with DNA, in DNA computers III, eds. H. Rubin and D. Wood, AMS DIMACS series, vol. 48, 123–135, (1999).
N. Jonoska, S. Karl, M. Saito, Three dimensional DNA structures in computing, BioSystems, 52, 143–153, (1999).
L. H. Kauffman, Knots and Physics, World Scientific, Series on knots and everything, vol. 1, 1991.
J. R. Munkres, Topology, a first course, Prentice-Hall, 1975.
J. R. Munkres, Elements of Algebraic Topology, Addison-Wesley Publ. Co., 1994.
Rolfsen, D., Knots and Links. Publish or Perish Press, (Berkley 1976).
N.C. Seeman, Physical Models for Exploring DNA Topology. Journal of Biomolecular Structure and Dynamics 5, 997–1004 (1988).
N.C. Seeman, Construction of Three-Dimensional Stick Figures From Branched DNA, DNA and Cell Biology 10 (1991), No. 7, 475–486.
N.C. Seeman, The design of single-stranded nucleic acid knots, Molecular Engineering 2, 297–307, (1992).
N. C. Seeman, Y. Zhang, S.M. Du and J. Chen, Construction of DNA polyhedra and knots through symmetry minimization, Supermolecular Stereochemistry, J. S. Siegel, ed., (1995), 27–32.
D.W. Sumners, ed., New Scientific Applications of Geometry and Topology, Proc. of Symposia in Applied Mathematics, Vol. 45, A.M.S., (1992).
J.W.T. Youngs, Minimal Imbeddings and the genus of a graph, J. of Math. Mech., vol. 12, (1963), 303–315.
S. A. Wasserman and N. R. Cozzarelli, Biochemical Topology: Applications to DNA recombination and replication. Science, vol. 232, (1986), 951–960.
E. Winfree, X. Yang, N.C. Seeman, Universal Computation via Self-assembry of DNA: Some Theory and Experiments. in DNA computers II, eds. L. Landweber and E. Baum, AMS DIMACS series, vol. 44, 191–214 (1998).
Winfree, F. Liu, L. A. Wenzler, and N.C. Seeman, Design and Self-Assembly of Two-Dimensional DNA Crystals, Nature 394 (1998), 539–544.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jonoska, N., Saito, M. (2002). Boundary Components of Thickened Graphs. In: Jonoska, N., Seeman, N.C. (eds) DNA Computing. DNA 2001. Lecture Notes in Computer Science, vol 2340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48017-X_7
Download citation
DOI: https://doi.org/10.1007/3-540-48017-X_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43775-8
Online ISBN: 978-3-540-48017-4
eBook Packages: Springer Book Archive