Molecular implementation of simple logic programs

1. Molecular implementation of simple logic programs FAB6 Tom Ran August 2010 Advisor: Ehud Shapiro

3. The Objective

4. The Objective • Programs describing things: • Life Science Data  Analyze\Model via Computer Science methods • Programs are things: • Computer Science Concepts Assimilate Life Science • Previously, molecular implementations of finite automata and logic gates were developed.

5. The Objective • Programs describing things: • Life Science Data  Analyze\Model via Computer Science methods • Programs are things: • Computer Science Concepts Implement via Life Science materials • Previously, molecular implementations of finite automata and logic gates were developed.

6. Mortal(X)  Man(X) Temporary(X)  Mortal(X) Immortal(X)  God(X) Man(Socrates) God(Zeus) Temporary(Socrates)? Compiling user’s high level language into assembly language Immortal(X)  God(X) Man(Socrates) God(Zeus) Temporary(Socrates)? Compiling assembly language into high level language

7. Mortal(X)  Man(X) Temporary(X)  Mortal(X) Immortal(X)  God(X) Man(Socrates) God(Zeus) Temporary(Socrates)? Compiling user’s high level language into molecular assembly language man(X)mortal(X) man(socrates) mortal(socrates)? Immortal(X)  God(X) Man(Socrates) God(Zeus) Temporary(Socrates)? man(heraclitus) Compiling molecular assembly language into high level language

8. Programs are things • Computational Concepts Molecular Implementation • Aristotelian syllogism (400 b.c.)

9. Motivation? • Biological-computers have the clear advantage over silicone-based computers of: • Size – injected into cells. • Inherently composed out of biological parts – easily interact with biological environments. • Thus holding the promise for future biological and medical applications.

10. Propositional logic programming • Propositions – p, q. • Queries – p?, q?. • Implications – pq, qr.

11. Query answer / reduction • q , q? Yes. • p?, pq Reduce p?to the query q? . • This query reduction is justified by the deduction rulemodus ponens: “Socrates is a Man” “Socrates is Mortal” if “Socrates is a Man” Therefore“Socrates is Mortal” q p if q _ Thereforep

12. Implementation • Propositions, Queries & Implications - All represented by short DNA molecules.

13. Proposition molecule • Proposition p: • Represented by a dsDNA molecule. • A sticky end representing p on one end. • A fluorophore with a matching quencher at its other end.

14. Query molecule • Query p?: • Represented by a dsDNA molecule. • A sticky end complementary to the representation of p. • A recognition site for the restriction enzyme FokI.

15. Reducing a query with a proposition • q? , q. Yes

16. Endonuclease II restriction enzyme - FokI 9 nt 13 nt Reducing a query with a proposition • q? , q. Yes

17. Reducing a query with a proposition • The sticky end of the query molecule q? hybridizes with that of the proposition molecule q.

18. Reducing a query with a proposition • FokI is attracted to its recognition site on the query and cleaves the proposition molecule q.

19. Reducing a query with a proposition • This results in the separation of its remaining sense and antisense strands, which in turn abolishes the quenching of the green fluorophore. • This green emission can be interpreted by an outside observer as a positive response to the query.

20. Reducing a query with a proposition • g

21. Reducing a query with a proposition

22. Reducing a query with a proposition

23. Reducing a query with a proposition

24. Implication molecule • Implication pq : • Represented by a hairpin ssDNA. • Sticky end representing the proposition p. • A segment complementary to the representation of q. • A segment that together with an auxiliary complementary strand forms a recognition site for FokI.

25. Reducing a query with an implication • The implication pq can be used to reduce the query p? to the query q? • Meaning that in order to positively answer p? it suffices to positively answer q?.

26. Reducing a query with an implication

27. Reducing a query with an implication

28. Reducing a query with an implication

29. Reducing a query with an implication

30. Reducing a query with an implication

31. Logic programming • We use the molecular logic system thus obtained to implement simple logic programs. • Logic programming is an approach to computer programming that uses a subset of First Order Logic as a programming language. • Has applications in AI research, natural language processing, and concurrent programming. • Here we focus on logic programs with unary predicates and simple implications.

32. Simple logic programs • Facts • Man(Socrates) • Man(Plato) • Philosopher(Plato) • Philosopher(Socrates) • Rules • Mortal(X)  Man(X) • Queries • Man(Socrates)? • Man(Plato)? • Philosopher(Plato)? • Mortal(Socrates)?

33. Propositional logic  Logic program • Logic program Facts such as Man(Socrates) are implemented as propositional implications "Man(X)"  "X=Socrates“. • Logic program Rules are implemented astheir corresponding implications. • Logic program Queries such as Mortal(Socrates) are implemented asa combination of the propositional assumption "X=Socrates" and the query "Mortal(X)"?.

34. A Logic program’s computation P: Rules: Mortal(X)Man(X) Facts: Man(Socartes) Q: Query: Mortal(Socartes)?

35. A Logic program’s computation Current query P: Rules: Mortal(X)Man(X) Facts: Man(Socartes) Q: Query: Mortal(Socartes)?

36. A Logic program’s computation Current query P: Rules: Mortal(X)Man(X) Facts: Man(Socartes) Mortal(Socrates)? Q: Query: Mortal(Socartes)?

37. A Logic program’s computation Current query P: Rules: Mortal(X)  Facts: Man(Socartes) Man(Socrates) Mortal(Socrates)? Q: Query: Mortal(Socartes)?

38. A Logic program’s computation Current query P: Rules: Mortal (X)Man (X) Facts: Man(Socartes) Man(Socrates)? Empty  Q: Query: Mortal(Socartes)?

39. A Logic program’s computation Current query Yes P: Rules: Mortal (X)Man (X) Facts: Man(Socartes) Q: Query: Mortal(Socartes)?

40. X=Socrates Mortal(X)? Auxiliary Man(X) Mortal(X)  Man(X)? Rules :Mortal(X)  Man(X)Facts :Man(Socrates)Query1:Mortal(Socrates)?Query2:Mortal (heraclitus)? X=Socrates? X=Socrates Man(X)  ? heraclitus’ Mortal(X)?

41. Auxiliary X=Socrates Mortal(X)? Man(X) Mortal(X)   Man(X)? X=Socrates? X=Socrates Man(X)  heraclitus’ Mortal(X)?

42. Auxiliary Man(X)? X=Socrates Mortal(X)? Man(X) Mortal(X)   Man(X)? Mortal(X)? X=Socrates? X=Socrates Man(X)  heraclitus’ Mortal(X)?

43. X=Socrates Man(X) Mortal(X)  Man(X)? Mortal(X)? X=Socrates? X=Socrates Man(X)  heraclitus’ Mortal(X)?

44. Auxiliary Man(X)? X=Socrates X=Socrates Man(X) Mortal(X)  Mortal(X)? X=Socrates? Socrates Man(X)  X=Socrates Man(X)? heraclitus’ Mortal(X)?

45. X=Socrates Man(X) Mortal(X)  Mortal(X)? X=Socrates? Socrates Man(X)  Man(X)? heraclitus’ Mortal(X)?

46. X=Socrates? X=Socrates Man(X) Mortal(X)  Mortal(X)? Socrates Man(X)  Man(X)? X=Socrates? heraclitus’ Mortal(X)? Yes

47. X=Socrates? Mortal(X)? Auxiliary Man(X) Mortal(X)  Man(X)? Rules :Mortal(X)  Man(X)Facts :Man(Socrates)Query1:Mortal(Socrates)?Query2:Mortal (Plato)? X=Socrates? X=Socrates Man(X)  X=Plato Mortal(X)? No

48. Answering a query - in full molecular-level detail Program: Man(Plato) Query: Man(Plato)?

49. Answering queries • The final results of 12 biochemical reactions of various combinations of queries and facts. • The dynamics of these reactions.

50. More elaborate deduction • A molecular logic program containing: • Mortal(X)Man(X) • Man(X)Greek(X) • Greek(Plato) • Molecular query : • Mortal(Plato)?