1. Molecular Computation : RNA solutions to chess problems Dirk Faulhammer, Anthony R. Cukras, Richard J. Lipton, and Laura F. Landweber PNAS 2000; vol. 97: no. 4: 1385-1389 2004.11.20 Summarized by Seong Hwan Kim

2. Table of Contents “Knight Problem” Key features Preparation before experiment Experiment Result Discussion

3. Knight Problem in Chess Game(1/2) ‘Knight ’ in chess game ? –A piece in the game, depicted as a horse’s head –Plays and captures alternatively on white and black square –“Jumping” available  ignore any pieces in its moving path –Powerful at the center position rather than edge

4. Knight Problem in Chess Game(2/2) ‘Knight Problem ’ ? –Knight tour problem –Hamiltonian path problem in graph theory a variant of knight problem –Asking a configuration of knights on a n x n chess board –such as ‘no knight is attacking any other knight on the board ’

5. Key features Applying molecular computation algorithm –To a 3x3 chessboard problem –Using RNA library –Searching RNA strands that fit the constraints Destructive algorithm with RNase H –Instead of conventional hybridization extraction –Hydrolyze RNA strands inappropriate for the solution constraints –Using hybridization of RNA and complementary bit DNA oligonucleotides as a hydrolysis marking

6. Preparation(1/6) : problem expression Knight problem expression –9 positions of 3x3 chessboard –‘no knight is attacking any other knight on the board ’ simplifying

7. Preparation(2/6) : solution expression RNA library –Made through synthesis of DNA “Half Libraries” –A RNA strand means 10-bit solution –Contain 1024 different strands –10-bit library for a instance of a 9-bit problem  Ignore any position that computes less reliably

8. Preparation(3/6) : Sequence Design 3 criteria 1) different bit encodings –Maximizing Hamming Distances between different strands as well as between different parts of individual strand –<= 5 matches over a 20-nt window, both within and between all 210 possible strands –Average melting temperature of 45 ℃ 2) Biased to avoid secondary structure –Each bit position, equally accessible to the enzyme and DNA –Using a three-letter alphabet : A, C, and U for the bits and for the bits and spacers in the library –Eliminating potential of G-C pair (G:U in RNA) as well as G stacking

9. Preparation(4/6) : Sequence Design 3 criteria (Cont’d) 3) constraint for hybridization –Avoid hybridization to themselves or to any other library strands by more than 7 consecutive base pairs –To avoid the interference made by inaccessibility of reagents to the regions Computer program for design –PERMUTE –Published as supplemental material on the PNAS web site, www.pnas.org www.pnas.org

10. Preparation(5/6) : Sequence Design Sequence Design Result 1) sequence for each bit and spacer of the DNA library

11. Preparation(6/6) : Sequence Design Sequence Design Result (Cont’d) 2) sequence for each DNA bit oligonucleotide

12. Experiment (1/6) : Library Synthesis 1)Synthesis of a 10-bit DNA library Recursive mix and split strategy Mix half libraries Primer extension 2)Synthesis of a 10 bit RNA library From the previously synthesized DNA library Synthesized by in vitro T7-transcription

13. Experiment (2/6) : Library Synthesis (Cont’d)  Modular construction of the combinatorial DNA library from two half-libraries –One half From bit ‘f’ through ‘a’ to ‘prefix’ –The other half From reverse complementary ‘f’ through ‘j’ to ‘suffix’ –White box for “true”, or “1” –Black box for “false”, or “0” –Shadowed box for prefix, suffix, and spacer sequences

14. Experiment (3/6) : RNA algorithm 1)Prepare a test tube containing RNA pool Initially encodes all 1024 possible 10-bit string ‘1’ or ‘0’ assigned to a specific bit position 2)Bit operation for a clause in the rule Dividing the initial RNA library into two test tubes One for RNA of having a value ‘1’ at a specific bit position The other for ‘0’ 3)Target digestion by RNase H Destroying inappropriate RNA strands in each tube Combining resulting two tubes 4)repeat 2)~3) for the next OR clause in the rule 5)Readout the surviving strands

15. Experiment (4/6) : RNA algorithm  Diagram for RNA algorithm which illustrating start from the proposition followed by other successive OR clauses in the rule

16. Experiment (5/6) : RNA algorithm 1)Digestion of the RNA library by thermostable RNase H RNase H digests RNA strands in the presence of combination of DNA bit oligonucleotides (a 0,f 1,h 1 ;b 0,g 1,i 1 ;…) 2)Spin-column chromatography and gel purification Remove DNA bit oligonucleotides and short RNA digestion products Remaining full-length RNA strands are purified by polyacrylamide gel 3)Reverse transcription and PCR Recovered RNA strands are reverse transcribed Amplified by no more than five PCR cycles to reduce recombination events Half of resulting DNA are transcribed in vitro for the next step in the algorithm 4)Readout by colony PCR followed multiplex linear PCR Creates a “bar code” for each strand Allow rapid screening and recovery of individual library strands

17. Experiment (6/6) : RNA algorithm (Cont’d)  Multiplex colony PCR readout

18. Result (1/3) : RNA solution Analysis 43 clones are randomly chosen and interpreted by readout PCR 42 of them, solution for this version of “knight problem” 10 solutions occur more than once Acquire 31 different solutions of unique board configuration with 1 illegal solution similar distribution as a random sampling of all 94 possible solutions (higher numbers of knights modestly preferred) Other 64 solution are all variants of 30 solutions

19. Result (2/3) : RNA solution Analysis (Cont’d)  31 unique boards  Expected and observed frequencies of boards

20. Result (3/3) : RNA solution Analysis (Cont’d) Illegal solution results from ineffective RNase H cleavage because of an adjacent deletion and point mutation in bit 9 (TCCACTACTACCTA instead of TCCACCAACTACCTA) Main source of error is clusters of mutations in the same bit positions Accurate size purification needed to reduce prevalence of such deletion

21. Discussion 2 50 ~ 10 15 : number of RNA molecules that in vitro selection protocols can currently search Upper bound for the size of DNA or RNA computing experiments that can use exhaustive search algorithm Same order as many interesting problem in computer science Further works : Knight tour problem, rule finding