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

Delve into cutting-edge DNA computing and research paradigms for autonomous molecular computers. Understand the transition from computation to structure construction, utilizing state machines and cellular automata. Dive into the complexities of implementing Boolean expressions through DNA molecules.

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

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  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.

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