Spectrum of a Pot for DNA Complexes

Given a set of flexible branched junction DNA molecules (building blocks) with sticky ends we consider the question of determining the proper stoichiometry such that all sticky ends could end up connected. The idea is to determine the proper proportion (spectrum) of each type of molecules present, which in general is not uniform. We classify the pot in three classes: weakly satisfiable, satisfiable and strongly satisfiable according to possible components that assemble in complete complexes. This classification is characterized through the spectrum of the pot, which can be computed in PTIME using the standard Gauss-Jordan elimination method.

[1]  N. Seeman,et al.  Ligation of triangles built from bulged 3-arm DNA branched junctions , 1996 .

[2]  David I. Lewin,et al.  DNA computing , 2002, Comput. Sci. Eng..

[3]  N. Jonoska,et al.  Three dimensional DNA structures in computing. , 1999, Bio Systems.

[4]  Sudheer Sahu,et al.  A Self-assembly Model of Time-Dependent Glue Strength , 2005, DNA.

[5]  William M. Shih,et al.  A 1.7-kilobase single-stranded DNA that folds into a nanoscale octahedron , 2004, Nature.

[6]  Natasa Jonoska,et al.  Expectation and Variance of Self-assembled Graph Structures , 2005, DNA.

[7]  Ashish Goel,et al.  Combinatorial optimization problems in self-assembly , 2002, STOC '02.

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

[9]  Jarkko Kari,et al.  On the decidability of self-assembly of infinite ribbons , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

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

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

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

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

[14]  Erik Winfree,et al.  The program-size complexity of self-assembled squares (extended abstract) , 2000, STOC '00.

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

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

[17]  Rob D. Coalson,et al.  Rotational Relaxation in Polar Solvents. Molecular Dynamics Study of Solute−Solvent Interaction , 1998 .

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

[19]  Ming-Yang Kao,et al.  DNA Self-Assembly For Constructing 3D Boxes , 2001, ISAAC.

[20]  R. Williams,et al.  Journal of American Chemical Society , 1979 .

[21]  Stuart A. Kurtz,et al.  Active transport in biological computing , 1996, DNA Based Computers.

[22]  Russell P. Goodman,et al.  Rapid Chiral Assembly of Rigid DNA Building Blocks for Molecular Nanofabrication , 2005, Science.