Towards Autonomous Molecular Computers Masami Hagiya, Proceedings of GP, 1997

1. Towards Autonomous Molecular ComputersMasami Hagiya, Proceedings of GP, 1997 2004. 11. 20. Nakjung Choi Email: fomula@mmlab.snu.ac.kr

2. Contents • DNA computing and accompanying research problem • Aldeman-Lipton Paradigm • Winfree’s Cellular Automata • DNA State Machines • From Computation to Structure Construction

3. 4 3 DHPP (directed Hamiltonian path problem) 1 0 6 2 5 0  1  2  3  4  5  6 DNA Computing and Accompanying Research Problems (1/3) • The Adleman-Lipton Paradigm [1][2] • One of data-parallel computation using DNA molecules • Combinational search problems by generating and testing paths represented by DNA molecules

4. DNA Computing and Accompanying Research Problems (2/3) • The Adleman-Lipton Paradigm • In the generating step • Candidates (about 1012) for a solution are randomly generated using hybridization between complementary sequences of DNA • In the testing step • Molecular biology techniques to check whether each candidate satisfies the conditions necessary for it to represent a solution (data-parallel computation)

5. DNA Computing and Accompanying Research Problems (3/3) • Reliability of Experimental Results • Physico-chemical consideration in the design of tube algorithms • Optimize the tube protocols • Problem Size • Presently, aim only to certify the feasibility • Remain relatively small (only 7 vertices in Adleman’s) • Experimental Costs • Autonomous computation by molecular reactions

6. [Tiling by DX units] Winfree’s Cellular Automata • A computational model [3] • Employ rectangular tiles made of DC units, each of which consists of four DNA molecules • Simulate computation of one-dimensional cellular automata by a tiling reaction of DX units in the two dimensional plane • Solve search problems such as the DHPP by having many tiling reactions proceed in parallel in a test tube (one-pot→autonomous)

7. Protocol DNA State Machines (1/5) • Successive Localized Polymerization • Transition table of a stat machine • A state transition is performed by the polymerization of a hairpin structure formed by a single strand

8. Input, program and state Transition table form DNA State Machines (2/5) • Computing Boolean Expressions • “Not only the input to the boolean expression but also the boolean expression itself is represented as a DNA molecule” • An input to a expression containing n variables

9. DNA State Machines (3/5) • Computing Boolean Expressions • Boolean expression example Implementation

10. DNA State Machines (4/5) • Computing Boolean Expressions • Restriction →each variable is allowed to occur only once • If the value of xi is true, then the next stat could be either var2 or output--. • Boolean expressions in which each variable occurs at most once are called “µ-formulas”. • If variable xi occurs twice in a boolean expression, a copy of xi, xi’ must be prepared, and the value of xi’ is also given in an input and must be identical to that of xi

11. Translation of µ-formulas DNA State Machines (5/5) • Computing Boolean Expressions • In Winfree’s paper [4], not only boolean expressions but also binary decision diagrams can be implemented The representation of µ-formulas eby computing trans(e, output+, output--)

12. From Computation to Structure Construction • Autonomous computation by molecular reactions • A method for constructing structures on the molecular scale • If one can construct complex structures out of DNA molecules, one can also organize other kinds of molecules guided by the structures of DNA

13. References • [1] Leonard M. Adleman: Molecular Computation of Solutions to Combinatorial Problems, Science, Vol.266, 1994, pp.1021-1024. • [2] Richard J. Lipton: DNA Solution of Hard Computational Problems, Science, Vol.268 1995, pp.542-545. • [3] Erik Winfree, Xiaoping Yang and Nadirian C. Seeman: Universal Computation via Self-assembly of DNA: Some Theory and Experiments, Second Annual Meeting on DNA Based Computers, June 10, 11, & 12, 1996, DIMACS Workshop, Princeton University, Dept. of Computer Science, pp.172-190. • [4] Erik Winfree: to be submitted to 4th DIMACS Workshop on DNA Based Computers, 1998.