Towards Autonomous Molecular Computers Towards Autonomous Molecular Computers Masami Hagiya, Proceedings of GP, Nakjung Choi

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

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 DHPP (directed Hamiltonian path problem) 0  1  2  3  4  5  6

DNA Computing and Accompanying Research Problems (2/3) The Adleman-Lipton Paradigm – In the generating step Candidates (about ) 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)

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

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) [Tiling by DX units]

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 Protocol

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 Input, program and state Transition table form

DNA State Machines (3/5) Computing Boolean Expressions – Boolean expression example Implementation

DNA State Machines (4/5) Computing Boolean Expressions – Restriction → each variable is allowed to occur only once If the value of x i is true, then the next stat could be either var 2 or output --. – Boolean expressions in which each variable occurs at most once are called “µ-formulas”. – If variable x i occurs twice in a boolean expression, a copy of x i, x i ’ must be prepared, and the value of x i ’ is also given in an input and must be identical to that of x i

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 Translation of µ-formulas The representation of µ-formulas e by computing trans(e, output +, output -- )

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

References [1] Leonard M. Adleman: Molecular Computation of Solutions to Combinatorial Problems, Science, Vol.266, 1994, pp [2] Richard J. Lipton: DNA Solution of Hard Computational Problems, Science, Vol , pp [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 [4] Erik Winfree: to be submitted to 4 th DIMACS Workshop on DNA Based Computers, 1998.