Computation by Self-assembly of DNA Graphs N. Jonoska, P. Sa-Ardyen, and N. Seeman Genetic Programming and Evolvable Machines, v.4, pp , 2003 Summarized by In-Hee Lee

Solving 3-SAT by DNA Graphs Associate a graph for a formula – Vertices: every clause, every variable and its negation. – Edges: between each variable and its negation, between clause and variable if the variable is contained in that clause.

Molecular Building Blocks Clause building block – 3-way junction – Sticky end contains truth value assignment which makes the clause 1. – We need 7 clause blocks for a clause. Variable building block – Multi-way junction – 2 blocks for a variable. …… + - # of clauses which contain positive variable # of clauses which contain negative variable

Molecular Building Blocks Clause building block Variable building block

Solving 3-SAT by Graphs A DNA graph is formed by the building blocks if and only if there is an assignment to the variables which makes the formula 1. The steps 1.Combine all building blocks and perform hybridization and ligation. 2.Determine where a DNA graph is formed. 1.Remove partially formed graphs. 2.Remove the graph that larger than the original graph. 3.If there is remaining structure, conclude that the formula is satisfiable. Otherwise, it is not satisfiable. 2-D gel electrophoresis was used. Why?

Solving 3-colorability Problem Same way as in the 3-SAT problem 3 vertex blocks (R,G,B) for each vertex in the graph. 6 edge blocks for each edge. If a DNA graph is formed, we solved the problem. Experimental steps are the same.

Graph & Building Blocks Graph to be colored Edge block Vertex block

Experimental Results for 3- Colorability Problem Design – Considered the physical position of each strands. – Positioned unique restriction site for each edge. – Designed by SEQUIN, DNASequenceGenerator. – Utilized pre-designed junction molecules (Seeman). – Expected size: 1078 bases