1. DNA Computing by Self Assembly  Erik Winfree, Caltech

2. Self Assembly of a Box

3. Information and Algorithms  Electronic microprocessors control electro-mechanical devices  Biochemical circuits control molecular/chemical events  General Goal: design biochemical algorithms/circuits that are programmable and can perform functions

4. Self Assembly Model  Model we will investigate: molecular self assembly of heterogeneous crystals  Idea: use periodic order of crystals to perform arbitrarily complex computation  What are purposes of self assembly?  2 main schools of thought

5. Purposes  1. Use massive parallelism of chemistry and lots of DNA at a time to solve difficult combinatorial optimization problems, such as SAT/TSP  2. Use self assembly algorithms to fabricate exact shapes / circuits/ patterns etc..

6. Precursors  Idea of self assembly arose from 3 ideas  1. DNA computing (Adleman 1994)  2. Tiling theory (Grun. & Shep. 1986)  3. DNA nanotechnology (Seeman 1982)

7. DNA Computing Adleman 1994 – Solved 6 node Hamiltonian Path Problem Nodes labeled with random 20mer Edge(u, v) = last 10 BP of u + first 10 BP of v

8. Hamiltonian Path Used DNA hybridization to generate random paths through graph Added programmable binding to impose conditions (start city, end city, num cities, no repeats..) 1 st meaningful computation by DNA Heralded as a landmark achievement

9. Steps of process  Generate random paths (DNA molecules) through graph  Use PCR to amplify all paths that start at first city and end at last city (use primers)  Test if path contains city 1. Amplify paths that pass test. Repeat tests for cities 2 through n.  If anything left, return YES. Else return NO.

10. Tiling Theory  Tiling – arrangement of basic shapes to cover infinite plane  Wang 1963 – Showed infinite num of square tiles with 4 colored sides can create Turing machine history  Wang Tiles are very powerful. Use DNA molecules to simulate Wang tiles in self assembly

11. DNA Nanotechnology Seeman 1982 – use DNA as a building block for nanostructures Block: Four armed DNA double-crossover molecules (DX) Label 4 arms of DX molecules with labels like Wang tiles

12. DX Molecule = Wang tile Adjacent tiles = sequences at sticky ends of 2 molecules go together Upper Right A = CATAC Lower Left B = GTATG

13. Simplified Tile Assembly Model  Given a set of possible tiles and possible bonds  4 sides of tile have bonds, bond has strength (0, 1,2)  2 tiles can bond together if their bonds fit, and if total strength (sums of bond strengths on common sides) is > threshold  Growth starts with a seed tile

14. Binary Counter Using 3 border tiles, 2 ‘0-bit’ tiles, 2 ‘1-bit’ tiles, can simulate a binary counter Power: only 7 tiles required

15. Experimental Demonstrations 1d array – Adleman DNA Computing1994 2d array – Winfree 1998 3d array – Open Next: Example of Winfree construction

16. XOR Practice Everyone try this out. Start with a 1 in a sea of 0’s. To generate next row, each tile checks its two neighbors, performs XOR and places the result below it in the next row XOR 00 = 0 11=0 01 = 110=1

17. XORing 000000000010000000000 000000000101000000000 000000001000100000000 000000010101010000000 000000100000001000000 000001010000010100000 000010001000100010000 000101010101010101000 001000000000000000100 ……..

18. Sierpinski Triangle 1 st 2d process to be experimentally demonstrated = Sierpinski Gasket Best result so far: 8 by 16 error-free triangle Poor results due to 1-10% tile binding error

19. Sample Tile Solution Slight variant of Sierpinski Triangle

20. Application 1: Solve NP hard problems  NP-complete problems: exponential number of solutions, hard to find correct solution, but easy to verify  Idea: Chemistry can generate all possible solutions and filter solutions quickly  Hack: Push exponential dimension of problem into volume of DNA needed  1 mL DNA = 2 60 bits of information

21. Apply self assembly  Let massive parallelism solve problem  In self assembly, generate input as initial set of tiles  See if Yes or No tile is produced at end

22. Current results  Problems solved – Hamiltonian Path, Satisfiability, etc..  Assuming no errors, 40- variable SAT needs 30 mL DNA and several hours  10 12 operations/second, inferior to computers  Winfree: No “low hanging fruit” for self assembly here

23. Application 2: Programmable Nanofabrication  Fabricate molecular electronic circuits  Current technology hitting the limit soon  Solution: create molecular structures like carbon nanotubes.  How to arrange tiny chemical components into fixed patterns?

24. Nanocircuits  Solution: Use self assembly to create molecular components  Small pieces such as NAND/OR gates can be created  Hard to create large microprocessors  Self assembly good to make circuits that have “concise” descriptions, eg recursive formulations

25. DNA Circuit Picture RAM Demultiplexer 2 bands = earlier bit counter example

26. Summary – Achievements  Robust, readily programmable  Dozens of crystals have been successfully used as DNA tiles  Self assembly has concrete experimental results, unlike other molecular computing technologies

27. Summary – Current Problems  Current DNA tiles distorted, 1% positioning error in experiments.  Size of tile is limited – all crystals < 10 microns.  1 – 10 % step error. eg tiles bond incorrectly quite often. Very big problem. => New model: error correcting tiles in self assembly

28. Yet more problems  Undesired nucleation – self assembly starts by itself  Problem occurs because biological system starts when it wants to minimize energy  Solution: Have programmable control of nucleation. Add energy barriers to force assembly to start with seed tile.

29. Future Questions  Natural question: What shapes can be made by self assembly?  Has parallels to Computability / Chomsky Language Theory  Minimum number of steps to make a shape?  Minimum number of tiles to make shape?

30. Final Thoughts  Although bio systems are like “circuits,” remember they: Contain large amounts of randomness Have very high error rates Contain hidden biological processes that cannot be described  So CS people don’t be surprised if experimental results are different from theoretical predictions

31. More thoughts  Winfree: We have already harnessed the electron to create electronic computers  No real progress has been made on chemical or nano computers  So: Algorithmic self assembly systems may be best best at next generation computers

32. Interested?  Winfree, E. 2003. DNA Computing by Self- Assembly. NAE's The Bridge, 33(4):31-38NAE's The Bridge  dna.caltech.edu  Contains a plethora of papers about numerous aspects of self assembly