1. Molecular Computing: Challenges across the two tracks in Theoretical Computer Science Masami Hagiya

2. Outline Japanese Molecular Computer Project –Adleman-Lipton Paradigm and Improvements Suyama’s Dynamic Programming DNA Computer –Autonomous Molecular Computing Sakamoto’s Hairpin Engines Analysis of Computational Power of Molecules Complexity of Molecular Computation Molecular Computation as Randomized Algorithm Towards New Computational Paradigms Molecular, Chemical, Cell, and Amorphous Computing Importance of Engineering Viewpoint --- Programming

3. Project Leader - Masami Hagiya (Computer Science) Members –Takashi Yokomori (Computer Science) –Masayuki Yamamura (Computer Science) –Masanori Arita (Genome Informatics) –Akira Suyama (Biophysics) –Yuzuru Husimi (Biophysics) –Kensaku Sakamoto (Biochemistry) –Shigeyuki Yokoyama (Biochemistry) October 1996 - March 2001 Funded by Japan Society for Promotion of Science –Research for the Future Program JSPS Project on Molecular Computing

4. Goals of Molecular Computing Analyses and Applications of Computational Power of Biomolecules –Understanding Life from the Viewpoint of Computation computational mystery of life –Life is computationally very efficient. –Engineering Applications (not restricted to computation) combinatorial optimization (computationally inspired) biotechnology nanotechnology, nanomachine cryptography medical and pharmaceutical applications in the future New Computational Model, New Simulation Technology

5. Related Fields Genome Informatics –applying computer science techniques to analyze genomic information –part of the human genome project –the other way round But genome informatics is a good application area for molecular computing. Quantum Computing –massively parallel computation by quantum superposition Artificial Life Artificial Molecular Evolution

6. Major Achievements of the Project Suyama’s Dynamic Programming DNA Computers –reduction of molecules by breadth-first search –automation by robots Sakamoto’s Hairpin Engines –Whiplash PCR and SAT Engine –molecular computation by hairpin formation –autonomous molecular computation Theoretical Studies by Yokomori’s Group Nishikawa’s Simulator for DNA computations Arita’s New Tool for Code Design Husimi’s 3SR-Based Evolutionary Reactor Yamamura’s Aqueous Computing (with Head)

7. Dynamic Programming DNA Computers

8. Adleman-Lipton Paradigm Adleman (Science 1994) –Solving Hamilton Path Problem by DNA Lipton, et al. –Solving SAT Problem by DNA Massively Parallel Computation by Molecules –Mainly for Combinatorial Optimization –Random Generation by Self-Assembly solution candidate ＝ DNA molecule –Selection by Molecular Biology Experiments Scaling Up ⇒ Efforts to increase yields and reduce errors Robot and Chemical IC

9. cf. Hamiltonian Path Problem by Adleman

10. Suyama’s Dynamic Programming DNA Computer “counting” （ Ogihara and Ray ） –O(2 0.4n ) molecules for n-variable 3-SAT “dynamic programming” （ Suyama ） Iteration of Generation and Selection –generation of candidates of partial solutions –selection of partial solutions The order of computational complexity does not decrease, but the amount of necessary molecules is drastically reduced. –3-SAT

11. DP algorithm for 3CNF-SAT on DNA Computers

12. 3-CNF SAT Solution on DP DNA Computer

13. DP algorithm for 3CNF-SAT )( 321 xxx  k’s loop: k ranges over variable indices j’s loop: j ranges over clause indices if x k is the 3 rd literal of the j-th clause then remove those assignments which satisfy neither the 1 st nor the 2 nd literal append X k F to the remaining assignments (do similarly if  x k is the 3 rd literal) X1T X2TX1T X2T X1F X2TX1F X2T X1T X2FX1T X2F X 1 F X 2 F k = 3 x 3 X1T X2F X3FX1T X2F X3F X1T X2T X3FX1T X2T X3F )( 321 xxx 

14. DP algorithm for 3CNF-SAT )( 321 xxx  k’s loop: k ranges over variable indices j’s loop: j ranges over clause indices if x k is the 3 rd literal of the j-th clause then remove those assignments which satisfy neither the 1 st nor the 2 nd literal append X k F to the remaining assignments (do similarly if  x k is the 3 rd literal) X1T X2TX1T X2T X1F X2TX1F X2T X1T X2FX1T X2F X 1 F X 2 F k = 3  x 3 X1FX2F X3TX1FX2F X3T X1F X2T X3TX1F X2T X3T )( 321 xxx 

15. DP algorithm for 3CNF-SAT )( 432 xxx  )( 432 xxx  )( 432 xxx  k’s loop: k ranges over variable indices j’s loop: j ranges over clause indices if x k is the 3 rd literal of the j-th clause then remove those assignments which satisfy neither the 1 st nor the 2 nd literal append X k F to the remaining assignments (do similarly if  x k is the 3 rd literal) X1F X2T X3TX1F X2T X3T X1F X2F X3TX1F X2F X3T X1T X2T X3FX1T X2T X3F X 1 T X 2 F X 3 F k = 4 x 4 X 1 T X 2 T X 3 F X 4 F

16. Implementation of Basic Operations annealing and ligation s s immobilization and cold wash s s hot wash s Taq DNA ligase get (T, +s), get (T, -s) s s annealing immobilization cold wash hot wash s get (T, +s) get (T, -s) s s amplify (T, T 1, T 2, …T n ) PCR immobilization and cold wash hot wash and divide annealing T T 1, T 2, …T n append (T, s, e) e e

17. On Scaling Up the Size of Computations Suyama’s estimation –2x10 -3 g of DNA for 100-variable 3-SAT 2x10 12 g of DNA by Adleman-Lipton –Current status: 4-variable 10-clause 3-SAT –Project goal: 30-variable 100-clause 3-SAT –Ultimate goal: 100-variable 400-clause 3-SAT Still, 100 variables are not many. A number of breakthroughs (in algorithms and experimental techniques) are required to defeat electronic computers. Robots, for example, …

18. Robot for DNA Computing Based on MAGTRATION TM

19. Automatic Operation of get Command on DNA Computer Robot get (T, +s), get (T, -s) s s annealing immobilization cold wash hot wash s get (T, +s) get (T, -s) s s

20. [Instrument] [Reset Counter] 0 [Home Position] 0 [MJ-Open Lid] ･･･ [Get1(0)] [Get2(1)] [Append(2)] ･･･ [Exit] protocol-level (1-1-4)[MJ-Open Lid] Do 2 _SEND"LID OPEN" Do10 _SEND"LID?" Wait_msec500 _CMP_GSTR"OPEN" IF_Goto EQ 0;open Wait_msec 1000 Loop ; Time out End ;open script-level Pascal/C-level Programming in DNA Computer

21. Hairpin Engines

22. Autonomous Molecular Computing Adleman-Lipton Paradigm –generation of candidates ＝ autonomous reaction –selection of solutions ＝ many operations from outside One-Pot Reaction ⇒ Autonomous Computation Comutation by Successive Autonomous Reactions by Molecules –Winfree’s DNA Tile –Sakamoto’s Hairpin Engines Whiplash PCR and SAT Engine Applications: –Nanotechnology, Nanomachine –(Computationally Inspired) Biotechnology

23. cf. Winfree’s DNA Tile

26. Hairpin Engines Molecular Computation by Hairpin Formation –Hairpin --- Typical Secondary Structure Whiplash PCR –DNA Automaton: State Machine by DNA –5 Transitions in a Control Experiment SAT Engine –Selection by Hairpin Structures of DNA –3 ‐ SAT: 6-Variable 10-Clause Formula

27. SAT Engine Sakamoto et al., Science, May 19, 2000. Selection by Hairpin Structures of DNA –digestion by restriction enzyme –exclusive PCR 3-SAT –ssDNA consisting of literals, each selected from a clause –complementary literal ＝ complementary sequence –detection of inconsistency ⇒ hairpin The essential part of the SAT computation is done by hairpin formation. –Autonomous Molecular Computation

28. b ￢b￢b e (a ∨ b ∨ c) ∧ ( ￢ d ∨ e ∨￢ f) ∧ … ∧ ( ￢ c ∨￢ b ∨ a) ∧... b ￢b￢b digestion by restriction enzyme exclusive PCR

30. Selection by Hairpin Structures Digestion by Restriction Enzyme –Hairpins are cut at the restriction site inserted in each literal sequence. Exclusive PCR –PCR is inefficient for hairpins. –In exclusive PCR, solution is diluted in each cycle to keep the difference in amplification. The number of steps is independent on the number of variables or clauses.

31. Generation of Random Pool (a∨b∨c)∧(d∨e∨f)∧(g∨h∨i)∧(j∨k∨l)(a∨b∨c)∧(d∨e∨f)∧(g∨h∨i)∧(j∨k∨l) adgj behk cfil Chemically Synthesized

32. Generation of Random Pool (a∨b∨c)∧(d∨e∨f)∧(g∨h∨i)∧(j∨k∨l)(a∨b∨c)∧(d∨e∨f)∧(g∨h∨i)∧(j∨k∨l) adgj behk cfil

33. (a∨b∨c)∧(d∨e∨f)∧(g∨h∨i)∧(j∨k∨l)(a∨b∨c)∧(d∨e∨f)∧(g∨h∨i)∧(j∨k∨l) a d g j b e h kc f il

34. 455544444498 BstXI BstNI 30 Generation of Random Pool 4

35. 6-Variable 10-Clause Formula (a ∨ b ∨ !c) ∧ (a ∨ c ∨ d) ∧ (a ∨ !c ∨ !d) ∧ (!a ∨ !c ∨ d) ∧ (a ∨ !c ∨ e) ∧ (a ∨ d ∨ !f) ∧ (!a ∨ c ∨ d) ∧ (a ∨ c ∨ !d) ∧ (!a ∨ !c ∨ !d) ∧ (!a ∨ c ∨ !d) ! = ￢

36. Solution of a 6-Variable 10-Clause formula

37. Whiplash PCR DNA Automaton ： State Machine by DNA –Polymerization of Hairpin –Polymerization Stop Autonomous MIMD Computation of Boolean μ-formulas Solving NP-Complete Problems in O(1)-Step e.g., vertex cover: vertex cover candidate ＝ transition table ＝ ssDNA vertex cover ＝ transition table that reaches the final state 5 Transitions in a Control Experiment

38. x BAx C B x ab Whiplash PCR

39. x BAx C B

40. x BAxCB x a

41. x BAxCB x a bc

44. 5 Transitions in a Control Experiment

45. 0 1 2 3 4 5 6 7

46. Analysis of Computational Power of Molecules

47. Complexity of Molecular Computation Time –Number of Laboratory Operations –Time for Each Operation more essential for the analysis of the computational power of molecules Space (= Parallelism) –Number of Molecules maximum number total number –Size (Length) of Molecules Analysis of the Trade-Off

48. Some Classical Results Reif (SPAA’95) –A nondeterministic Turing machine computation with input size n, space s and time 2 O(s) can be executed in our PAM Model using O(s) PA-Match steps and O(s log s) other PAM steps, employing aggregates of length O(s). Beaver (DNA1, 1995) –Polynomial-step molecular computers compute PSPACE. Rooß and Wagner (I&C, 1996) –Exactly the problems in P NP =  p 2 can be solved in polynomial time using Lipton’s model.

49. Yield and Error in Reactions Yield –equilibrium--- equilibrium constant (K) –time to reach equilibrium --- reaction constant (k) –example: A  [B] = (K/(1+K))(1  e  (k+k  1 ) t ) K = k/k  1 Error –example: mis-hybridization –Error probability is never zero.

50. Reduction of Errors Iteration of Laboratory Operations –increase in computation time –increase in loss of molecules increase in number of molecules Reduction of Error Probability –appropriate conditions temperature, salt concentration Low temperature leads to frequent mis-hybridzation. However, high temperature decreases the yield. –good encoding A number of papers have been published for designing good encoding.

51. Some Analyses Karp, Keynon and Waarts (SODA’96) –The number of extract operations required for achieving error-resilient bit evaluation is  (  log   log   ). Kurtz (DNA2, 1996) –thermodynamical analysis of path formation in Adleman’s experiment –time needed to form a Hamiltonian path ---  (n 2 ) Winfree (1998, Ph.D. Thesis) –thermodynamical analysis of DNA Tiling Rose, et al. (GECCO’99) –Computational Incoherency (thermodynamical analysis of mis-hybridization)

52. Efficiency of SAT Engine: Tentative Analysis Parameters – n : number of clauses –  : the probability that a satisfying assignment cannot be detected Orders –TimeO(n 2.5 ) –Number of Molecules O(4 n ln(1/  ))

53. Molecular Computation and Randomized Algorithms Randomized Algorithms with Molecules –Massive Parallelism –Random Operations very easy to implement by chemical reactions Error in Non-Random Operations –Error in non-random operations should not damage the error reducibility of a randomized algorithm. –Error should be compensated by random operations.

54. Some Recent Results Chen and Ramachandran (DNA6, 2000) –k-SAT by Paturi et al. Díaz, Esteban and Ogihara (DNA6, 2000) –k-SAT by Schöning Sakakibara (DNA6, 2000) –PAC Learning of DNF Formulas –Approximate Consistent Learning

55. Towards New Computational Paradigms

56. New Computational Paradigms Molecular Computing Chemical Computing Crystal Computing Cell Computing Gel Computing Amorphous Computing …

57. New Computational Paradigms Computation inside a Single Molecule Computation by Molecular Interactions Computation with Membranes Computation with Geometry Each paradigm is a rich source of computational power. They are strongly related with one another.

58. Computation inside a Single Molecule Computation by Conformational Change (Structure Formation) –Whiplash PCR (Sakamoto, et al.) –SAT Engine (Sakamoto, et al.) –NP-Completeness of Protein Folding (Fraenkel) Computation by Modification –Stickers Model (Roweis, et al.) –Aqueous Computing (Head and Yamamura) write-once molecular memory

59. Computation by Molecular Interactions Computation by Self-Assembly –DNA hybridization --- everywhere in DNA computing –DNA tiling (Winfree, et al.) Computation by Cutting and Pasting –restriction enzymes and ligase --- everywhere in DNA computing –H Systems --- Splicing Systems (Head) Self-Assembly and Conformational Change –Self-Assembling Automaton (Saitou) –YAC (Yokomori) Concurrency Calculi (without Membranes) Abstract Chemistry in Artificial Life

60. Recent Results in Computation by Self-Assembly Rothemund and Winfree (STOC 2000) –For any f (N) non-decreasing unbounded computable functions, the number of tiles required for the self-assembly of an N  N square is bounded infinitely often by f (N). Winfree, Eng and Rozenberg (DNA6, 2000) –Linear assembly of string tiles can generate the output languages of finite-visit Turing Machines.

61. Computation with Membranes Computation with Compartments –Chemical IC (MEMS) –Liposomes –P Systems (Paun) –Concurrency Calculi chemical abstract machine,  -calculus, join calculus ambient calculus Computation by Cells computation by gene regulation, signal transduction, and metabolism

62. Computation with Geometry Computation with Compartments –inside-or-outside topology Computation in Gel/on Surface –two kinds of molecule: immobile and mobile DNA Crystals --- DNA Tiling –2D or 3D topology (lattice) Amorphous Computing (Abelson, Knight and Sussman) –2D or 3D topology (continuous) –Computational Particles generation of coordinate systems GPL (growth-point language) –Cellular Computing (Weiss and Knight)

63. Importance of Engineering Viewpoint --- Programming Not Only Analysis but Also Synthesis –Sharp Distinction from Previous Studies: mathematical biology complex systems Synthesis = Programming –Design and Engineering of Artificial Systems Importance of Engineering Applications –Milestones of Research –Source of Motivations –Not Restricted to Computation nanotechnology biotechnology (computatinally inspired biotechnology)

64. Challenges New Computational Paradigms New Computational Models New Programming Languages New Applications These challenges should be simultaneously attacked with the progress of implementation techniques.