a field, in which little has been done, but in which an enormous amount can be done in principle

2 There's Plenty of Room at the Bottom Richard P. Feynman, 1959 a field, in which little has been done, but in which an enormous amount can be done in principle Nanoworld (1 m = 10 9 nm) Nanofabrication Nanocomputation Nanorobotics Nanoelectronics Nanodiagnostics/ therapeutics

3 There's Plenty of Room at the Bottom Nanoworld (1 m = 10 9 nm)?

4 There's Plenty of Room at the Bottom Nanoworld (1 m = 10 9 nm) How to build things? How to make things move (and do work)? How to compute?

5 DNA 101: DNA Not merely secret to life Information encoding: bases: A, T, C, G Complementarity of bases: A T; C G Complementary single strands 3.4 nm Duplex Self-Assembly! 2 nm

6 DNA 101: Self-assembly Single strand DNA as Smart glues (Excerpted from Seeman 03)

7 DNA Based Self-Assembly & Nano-Device: Theory & Practice DNA Based How to build? Self-Assembly How to move? Nano-Device How to compute? Theory & Practice Theoretical Design Mathematical Analysis Computer Modeling Biochem.. Lab Fabrication

8 Roadmap: DNA Based Self-Assembly & Nano-Device Complexity of Self-Assembly Error Resilient Self-Assembly Nanorobotics Device Nanocomputing Device

Self-Assembly Complexity - Error Correction Nanorobotics - Nanocomputing 10

11 Accretive Graph Assembly System Seed vertex Temperature Graph Weight function Temperature: τ = 2 Sequentially constructible? Seed vertex

12 Problems, Results, & Contributions Problems Accretive Graph Assembly Problem Self-Destructible Graph Assembly Prob. Results AGAP is NP-complete Planar AGAP is NP-complete #AGAP/Stochastic AGAP is #P-complete DGAP is PSPACE-complete Contributions Cooperative effects of attraction and repulsion General setting of graphs Dynamic self-destructible behavior in DGAP model

Complexity - Error Correction Nanorobotics Nanocomputing 13 Roadmap: DNA Based Self-Assembly & Nano-Device Complexity of Self-Assembly Error Resilient Self-Assembly Nanorobotics Device Nanocomputing Device

Self-Assembly Complexity - Error Correction Nanorobotics Nanocomputing 14

Complexity - Error Correction Nanorobotics Nanocomputing 15 Computational Tilings Tile (Excerpted from Yan et al 03) Computational tiles (Winfree) Pad Output 2 Output 1 Input 2 Input 1 Output 1 = Input 1 XOR Input 2 Output 2 = Input 1 AND Input 2

Binary counter Complexity - Error Correction Nanorobotics Nanocomputing 16 Binary counter Computational tiles Seed tile Frame tiles

Complexity - Error Correction Nanorobotics Nanocomputing Error in Assembly 17 Binary counter Computational tiles Seed tile Error! Frame tiles

Complexity - Error Correction Nanorobotics Nanocomputing 18 Error Resilient Tilings by Winfree Original tiles: Error resilient tiles: (Excerpted from Winfree 03) Error rate 2 Assembly size increased by 4

Complexity - Error Correction Nanorobotics Nanocomputing Compact Error Resilient Computational Tiles 19 Original tiles: X Y Z Error resilient tiles: XY YZ

Complexity - Error Correction Nanorobotics Nanocomputing Compact Error Resilient Computational Tiles 20 Original tiles: X Y Z Error resilient tiles: XY YZ

Complexity - Error Correction Nanorobotics Nanocomputing Compact Error Resilient Computational Tiles 21 Original tiles: X Y Z Error resilient tiles: XY YZ Error checking pads Assembly size not increased Two way overlay: error rate (5%) 2 (0.25%) Three way overlay: error rate (5%) 3 (0.0125%)

Complexity - Error Correction Nanorobotics Nanocomputing Computer Simulation (Xgrow, Winfree) 22 Three way overlay Winfree 3x3 construction Winfree 2x2 construction Two way overlay No error correction

Nano-Device Complexity - Error Correction Nanorobotics - Nanocomputing 24 (R. Cross Lab)

Autonomous Unidirectional DNA Walker: Design 25 Restriction enzymes Ligase PflM I Walker A * Anchorage B C D A BstAP I Track

DNA 101: Enzyme Ligation, Restriction 26 Sticky ends DNA ligase DNA restriction enzyme

DNA Walker: Operation 27 Valid hybridization: A* + B = A + B* A*B B* + C = B + C* B*C C* + D = C + D* C*D D* + A = D + A* D*A Valid cut: A*B A + B* B*C B + C* C*D C + D* D*A D + A* Walker A * Anchorage B C D A Track

DNA Walker: Operation 28 Valid hybridization: A* + B = A + B* A*B B* + C = B + C* B*C C* + D = C + D* C*D D* + A = D + A* D*A Valid cut: A*B A + B* B*C B + C* C*D C + D* D*A D + A* Ligase A*B C D A

DNA Walker: Operation 29 Valid hybridization: A* + B = A + B* A*B B* + C = B + C* B*C C* + D = C + D* C*D D* + A = D + A* D*A Valid cut: A*B A + B* B*C B + C* C*D C + D* D*A D + A* Ligase A*B C D A

DNA Walker: Operation 30 Valid hybridization: A* + B = A + B* A*B B* + C = B + C* B*C C* + D = C + D* C*D D* + A = D + A* D*A Valid cut: A*B A + B* B*C B + C* C*D C + D* D*A D + A* PflM I A*B C D A

31 DNA Walker: Operation Valid hybridization: A* + B = A + B* A*B B* + C = B + C* B*C C* + D = C + D* C*D D* + A = D + A* D*A Valid cut: A*B A + B* B*C B + C* C*D C + D* D*A D + A* B* A C D A

DNA Walker: Operation 32 Valid hybridization: A* + B = A + B* A*B B* + C = B + C* B*C C* + D = C + D* C*D D* + A = D + A* D*A Valid cut: A*B A + B* B*C B + C* C*D C + D* D*A D + A* Ligase A B*C D A

DNA Walker: Operation 33 Valid hybridization: A* + B = A + B* A*B B* + C = B + C* B*C C* + D = C + D* C*D D* + A = D + A* D*A Valid cut: A*B A + B* B*C B + C* C*D C + D* D*A D + A* Ligase A B*C D A

DNA Walker: Operation 34 Valid hybridization: A* + B = A + B* A*B B* + C = B + C* B*C C* + D = C + D* C*D D* + A = D + A* D*A Valid cut: A*B A + B* B*C B + C* C*D C + D* D*A D + A* BstAP I A B*C D A

35 DNA Walker: Operation Valid hybridization: A* + B = A + B* A*B B* + C = B + C* B*C C* + D = C + D* C*D D* + A = D + A* D*A Valid cut: A*B A + B* B*C B + C* C*D C + D* D*A D + A* C* A B D A

DNA Walker: Operation 36 Valid hybridization: A* + B = A + B* A*B B* + C = B + C* B*C C* + D = C + D* C*D D* + A = D + A* D*A Valid cut: A*B A + B* B*C B + C* C*D C + D* D*A D + A* A B C*D A

37 DNA Walker: Operation Valid hybridization: A* + B = A + B* A*B B* + C = B + C* B*C C* + D = C + D* C*D D* + A = D + A* D*A Valid cut: A*B A + B* B*C B + C* C*D C + D* D*A D + A* A B C A D*

DNA Walker: Operation 38 Valid hybridization: A* + B = A + B* A*B B* + C = B + C* B*C C* + D = C + D* C*D D* + A = D + A* D*A Valid cut: A*B A + B* B*C B + C* C*D C + D* D*A D + A* A B C D*A

DNA Walker: Operation 39 Valid hybridization: A* + B = A + B* A*B B* + C = B + C* B*C C* + D = C + D* C*D D* + A = D + A* D*A Valid cut: A*B A + B* B*C B + C* C*D C + D* D*A D + A* A B C D A*

DNA Walker: Experimental Design 40

Autonomous Motion of the Walker 41

Nano-Device Complexity - Error Correction Nanorobotics - Nanocomputing 43

DNA Cellular Computing Devices 44 Self-assembly Nanorobotics Nanocomputation (Yan et al 03) (Benenson et al 03) Complex motion Intelligent robotics devices Reusable DNA computers

DNA Cellular Computing Devices 45 Finite state automata Turing machine Cellular automata

Comp 101: Turing Machine 46 Read/write head Tape Transition rule

DNA Turing Machine: Structure 47 Turing machine Transition table: Rule molecules Turing head: Head molecules Data tape: Symbol molecules Autonomous universal DNA Turing machine: 2 states, 5 colors

Turing Machine: Operation 48 Turing machine

Turing Machine: Operation 49

Turing Machine: Molecule Set 55

Turing Machine: Molecule Set/Simulation 56 2 -Digit Binary Counter

Summary & Future 57 Summary: Complexity & Fault-Tolerance Robotics & Computing Future: Mathematical Theory: General theory & Dynamic behavior Fault-Tolerance: Inspirations from fault tolerance theory & Biological systems Robotics Devices: Robotics lattice & Nanoparticle carrying/(un)loading Computing Devices: In silicon in vitro in vivo: Doctor in a cell Software Tools: Molecular compiler - Rational design & Simulation

Summary & Summary: Complexity - Error Correction Nanorobotics - Nanocomputing Future 58 58 Complexity & Fault-Tolerance Robotics & Computing? Mathematical Theory: General theory & Dynamic behavior Fault-Tolerance: Fault tolerant theory & Biological inspiration Robotics Devices: Robotics lattice & Nanoparticle carrying/(un)loading Computing Devices: Intelligent robotics lattice & Doctor in a cell Software Tools: Molecular compiler - Rational design & Simulation Future: There's Plenty of Room at the Bottom!