1. Phillip Senum University of Minnesota

2. Motivation Much effort has been spent developing techniques for analyzing existing chemical systems. Comparatively little has been devoted to designing chemical systems. Seek to demonstrate that chemical systems can compute mathematical and logical functions.

3. Abstract/Conceptual Designs Microprocessors: Physical implementation with transistors. Theoretical implementation with logic gates. We can apply a similar level of abstraction to the design of biochemical system: Physical implementation with chemical reactions. Theoretical implementation using “modules.”

4. 12 6 TIMES TWO

5. 90 45 TIMES TWO

8. Design Objectives Minimal number of chemical reactions. Coarse rate categories: “Fast” “Slow” Each module has its own enable signal (and so is synchronizable). Results are exact.

9. Chemical Model Discrete chemical kinetics: “Variables” are molecular types. Validation via stochastic simulation: Gillespie’s method.

10. Building Blocks Inversion Duplication Incrementation/Decrementation Comparison

11. Inversion Produce a quantity of a species in the absence of another specific species.

12. Inversion a a ab a ab

13. Duplication Produce a quantity of a new species equal to the original population of the source species without permanently modifying the source.

14. y’ Duplication ygzy

16. TrialFast : SlowTrajectories gyz Expected zRel. Error 11005005100102.451002.45% 2100050050100104.8261004.83% 310005005100100.3121000.31% 41000050050100100.5161000.52% 5100005005100100.0221000.02% 61000050050100100.0341000.03% 710000500550004938.3950001.23% 8100005005050004967.2650000.65% 91000050020050004796.3850004.07% 1010000500502220.00%

17. Incrementation/Decrementation Add or subtract one from the population of a species:

18. Decrement x x’xg X 0 = 5

19. Decrement x x’ x x rx X 0 = 5

20. Decrement x x’ x x x rx X 0 = 5

21. x’ x xx x rx X 0 = 5 Decrement x

22. x’ x xx x x rx X 0 = 5

23. Decrement x x’ xx x x x rx X 0 = 5 X f = 4

25. Comparison Compare the initial quantities of two species and produce a species if the requested condition is true. Either a or b will remain. Presence or absence of each can be used to check if a condition is true. E.g. If a and b are initially equal, both will be completely consumed.

26. Comparison a b bbb b b b b a a a aa aa a ab b ab t t t

27. Comparison Logical comparisons of any type can be performed.

28. Combining Modules By cascading modules, we can perform more complex operations: Multiplication Logarithm Exponentiation Raise to a Power

29. Multiplication Can be implemented with iterative addition: Can be done with a “decrement” and a “copy” operation.

30. Multiplication START X > 0 Copy Y to Z Decrement X STOP FALSE TRUE

31. Multiplication

32. TrialFast : SlowTrajectories xyz Expected z Rel. Error 1100 504954.3550000.91% 2100 501004893.1850002.14% 31000100 504991.5650000.17% 41000100501004995.7850000.08% 510000100 504998.6950000.03% 610000100501004999.1450000.02% 7100001001020200.042000.02% 8100001002010200.032000.02%

33. Logarithm

34. Exponentiation

35. Raise to a Power

36. Defining a System Definition by a simple pseudo-code: Assignments Addition and subtraction Constants Variables “If” and “While” Nesting is okay

37. Future Research Build a compiler to translate pseudo-code into chemical reaction set. Implementation via DNA strand displacement Soloveichik D, Seelig G, Winfree E (2010) DNA as a universal substrate for chemical kinetics. Proceedings of the National Academy of Sciences 107: 5393-5398.

38. 12…3 1*3*… 2* 3*… a b

39. 12…3 1*3*…2* 3*… c waste

40. Acknowledgements Collaborators: Marc Riedel Sasha Kharam Hua Jiang Financial Support: University of Minnesota National Science Foundation National Library of Medicine/NIH PSB organizers