Forbidding - Enforcing Conditions in DNA Self-assembly of Graphs

This chapter suggests new directions in both graph theory and DNA self-assembly. The general problem faced here is the following: given a set P of paths and cycles, a set ℱ of forbidden structures, and a set ℰ of enforced structures, what are the graphs included in the set G(Γ) for Γ = (V, P, E, λ, ℱ, ℰ)? The model presented focuses in particular on DNA self-assembly and the set of structures obtained through this process. However, the idea of graph forbidding-enforcing systems can certainly be extended to other self-assembly processes in nature, as well as to the pure theoretical methods used to study the mathematical properties of graphs. In the case of DNA self-assembly, the evolution process is described in a very natural way as an increase in the cardinality of the matching set between vertices with complementary labels. For other types of applications, the concept of g-f-e systems may need to be adjusted in a different way that will be more suitable for simulating the evolution in those particular processes.

[1]  Natasa Jonoska,et al.  A Computational Model for Self-assembling Flexible Tiles , 2005, UC.

[2]  N. Seeman,et al.  Synthesis from DNA of a molecule with the connectivity of a cube , 1991, Nature.

[3]  Natasa Jonoska,et al.  Forbidding and enforcing in membrane computing , 2004, Natural Computing.

[4]  N C Seeman,et al.  Assembly and characterization of five-arm and six-arm DNA branched junctions. , 1991, Biochemistry.

[5]  E. Winfree,et al.  Algorithmic Self-Assembly of DNA Sierpinski Triangles , 2004, PLoS biology.

[6]  N. Seeman,et al.  Designed Two-Dimensional DNA Holliday Junction Arrays Visualized by Atomic Force Microscopy , 1999 .

[7]  Erik Winfree,et al.  Universal computation via self-assembly of DNA: Some theory and experiments , 1996, DNA Based Computers.

[8]  Natasa Jonoska,et al.  Computation by Self-assembly of DNA Graphs , 2004, Genetic Programming and Evolvable Machines.

[9]  M. Sahani,et al.  Algorithmic Self-Assembly of DNA , 2006 .

[10]  N C Seeman,et al.  Gel electrophoretic analysis of DNA branched junctions , 1989, Electrophoresis.

[11]  J. Reif,et al.  Construction, analysis, ligation, and self-assembly of DNA triple crossover complexes , 2000 .

[12]  Erik Winfree,et al.  Complexity of Self-assembled Shapes , 2004, DNA.

[13]  N. Seeman,et al.  Assembly of Borromean rings from DNA , 1997, Nature.

[14]  K Sakamoto,et al.  Molecular computation by DNA hairpin formation. , 2000, Science.

[15]  N. Seeman,et al.  A robust DNA mechanical device controlled by hybridization topology , 2002, Nature.

[16]  A. Turberfield,et al.  A DNA-fuelled molecular machine made of DNA , 2022 .

[17]  Alessandra Carbone,et al.  Coding and geometrical shapes in nanostructures: A fractal DNA-assembly , 2004, Natural Computing.

[18]  Sudheer Sahu,et al.  Complexity of graph self-assembly in accretive systems and self-destructible systems , 2005, Theor. Comput. Sci..

[19]  Natasa Jonoska,et al.  Boundary Components of Thickened Graphs , 2001, DNA.

[20]  N. Seeman,et al.  Design and self-assembly of two-dimensional DNA crystals , 1998, Nature.

[21]  J. Reif,et al.  Logical computation using algorithmic self-assembly of DNA triple-crossover molecules , 2000, Nature.

[22]  Natasha Jonoska,et al.  Self-assembly of irregular graphs whose edges are DNA helix axes. , 2004, Journal of the American Chemical Society.

[23]  N. Seeman,et al.  Construction of a DNA-Truncated Octahedron , 1994 .

[24]  Andrzej Ehrenfeucht,et al.  Forbidding-enforcing systems , 2003, Theor. Comput. Sci..

[25]  Alessandra Carbone,et al.  Circuits and programmable self-assembling DNA structures , 2002, Proceedings of the National Academy of Sciences of the United States of America.