Branching in Biological Models of Computation

1. Branching in Biological Models of Computation Blair Andres-Beck, Vera Bereg, Stephanie Lee, Mike Lindmark, Wojciech Makowiecki

2. Branching in DNA Computation • We chose several models of DNA computation and examined the implementation of if…else statements and looping • Allow easier mapping of conventional algorithms

3. Design Criteria • Any change must preserve the existing functionality of the model • Branching • Operation selection based on current data and instruction • Looping • Further instructions based on test condition • Nested loops; that is, looping that doesn’t rely on a single marker

4. The Sticker Model • Presented in “A Sticker Based Model for DNA Computation” (1996) • Two types of single stranded DNA molecules • memory strand • complimentary stickers • Four operations allow universal computation • set, clear, separate and combine

5. Bit Representation

6. Set and Clear

7. Combine and Separate

8. Simple branching and looping in the Sticker Model Idea: use current mechanical operations to do branching (if else) and looping

9. Branching with existing operations • Perform a separate based on branch condition • Act on each vial independently • “If” statement carried out on true, “else” on false • Recombine vials after “if” statement

10. Branching and Looping procedures

11. Looping with existing operations • Test for loop condition • Fluorescent markers • Can be detected by the robotic assistant • Can have more than one type, allowing nested looping • Choose next instruction based on presence or absence of fluorescence • Problems • Slow • Reliance on intervention outside the model

12. Implementation of Branching in DNA Transcriptional Logic Idea: use an OR gate for branching 

13. DNA Transcriptional Logic • How it works • Transcription factor binds to the promoter region • Activates the enzyme RNA Polymerase [RNAP] • Unzips DNA and produces programmable output

14. Implementation of Branching The OR gate allows the if-else statement to end and the program to continue

15. Definition of Branching • Branching allows for conditional if-else statements • {if (condition) {output 1}; else {output 2}; } continuation …

16. Pros Easy to track progress Does not require outside intervention Cons Does not allow parallelism Inefficient and fairly slow Requires large number of promoter -transcription factor pairs Properties of the Branching

17. “Smart” drug or DNA automata combined with Sticker Model Idea: use “if else” statements from “Smart” drug model (with stickers instead of drugs)

18. Automata • Automata • Machine that accepts strings over specific alphabet that are in its language • Computation terminates on processing last string symbol • Accepts input if terminates in accepting state

19. “Smart” Drug • Automata with: • Hardware (restriction nuclease, ligase) • Software (dsDNA with a hairpin structure at end) • In vitro

20. “Smart” Drug • Basic Idea: transport diagnosis and drug delivery (suppression) stages into the cell • No robotic intervention what-so-ever • Basic “if else” statements, thus can do branching! 

21. “Smart” Drug

22. “Smart” drug and Sticker Model • Sticker model: • Memory strand with on/off regions for bits • Drug model: • Code with a sticker as hairpin (software) • Reusable “rules” (hardware) • If (rule=true)  release sticker • Can do anti-stickers to clear off bits as well  • Thus SISD model • By varying code and subset of “rules” can change the outcome of the computation

23. Pros and Cons • Less mechanical operations used • Separation procedure might not be needed • Could possibly get rid of them all together? • Eliminates one of the positive sides of sticker model (no enzymes), but our enzymes are reusable (hardware) • Have SISD, can do MIMD? • How to ensure that each code is related to its specific data molecule?

24. Branching in the Sticker Model using DNA Instructions The Idea: Store the program with the data, run all the programs independently.

25. Basic Ideas • Encode instructions into DNA • Create a DNA program counter • Each DNA computes cycle: • Separate strands based on next instruction • Perform operation • Increment PC

26. Changes to the Sticker Model • Instruction strand = head + instruction + … + data connector • Instruction = instr code + operand code

27. Changes to the Sticker Model • Add connector to data strand • Addition of PC strands

28. Changes to the Sticker Model • Introduction of halt • No explicit combine or separate operations • Use of operation selectors

29. Adding Looping • Looping by restarting the PC • Loop operation • Clears off PC using complement PC strands if (stage1) { … if (NOT done) { loop; } … stage1 = false; }

30. Adding Branching • Add IF instruction code • Use End-If IF operation • Operation selectors with solid-bound stickers • Trapped strands enter branching cycle • Addition of excess PC and Step strands (excluding PC End-If IF strands) • Flow by End-If IF selectors • Return trapped strands

31. The Strands

32. Advantages • Reusability of data, pc, start, step, and selector strands • Simple programmability • Imagine building strand from instruction pieces • Ability to run more than one program concurrently • Thousands of problems at the same time

33. Disadvantages • Large error rate vs. long cycle time • Must perform several separations per cycle • No ability to do error correction • Large number of unique sequences needed

34. References • A Sticker Based Architecture for DNA Computation. Roweis, Sam, et. al. 7/96. • Lauria, Mario, Kaustubh Bhalerao, Muthu M. Pugalanthiran, and Bo Yuan. “Building blocks of a biochemical CPU based on DNA transcription logic.” 3rd Workshop on Non-Silicon Computation (NSC-3), Munich, June 2004. • Molecular Beacons: A Novel DNA Probe for Nucleic Acid and Protein Studies. W. Tan et al. • Molecular beacons attached to glass beads fluoresce upon hybridization to target DNA. L.Brown et al. • Automata Make Antisense. Condon, Anne. Nature, vol 429, p351. • Programmable and Autonomous Computing Machine Made of Biomolecules. Y. Benenson, T. Paz-Elizur, R. Adar, E. Keinan, Z. Livneh, E. Shapiro. Nature, vol. 414, p430. • An Autonomous Molecular Computer for Logical Control of Gene Expression. Y. Benenson, B. Gil, U. Ben-Dor, R. Adar, E. Shapiro. Nature, vol.429, p432.

36. The Strands

37. Execution Cycle Revisited • Initial Setup • Random input bits set • Add instruction strands, start strands • Execution Cycle • Flow strands by operation selector chambers • Seal chambers, perform operation • Collect, add PC strands • Wash PC strands, add step strands

38. Adding Branching • Add IF instruction code where operand is the condition bit • Use End-If IF operation • Operation selectors with solid-bound stickers • Proper length to require both connections to stick

39. Adding Branching • Trapped strands enter branching cycle • Addition of excess PC and Step strands (excluding PC End-If IF strands) • Flow by End-If IF selectors • Return trapped strands • Simple to get OR and NOT conditions • ie. OR = clear c; set n; if a; set c; end-if if n; if b; set c; end-if if n;

40. Fluorescent markers