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

㻧㻱㻤㻃㻥㼄㼖㼈㼇 㻃㻶㼈㼏㼉㻐㻤㼖㼖㼈㼐 㼅 㼏㼜㻃㼄㼑㼇 㻃㻃㻱㼄㼑㼒 㻐㻧㼈㼙㼌㼆㼈㻝

㻷㼋㼈㼒㼕㼜㻃㼄㼑㼇 㻃㻳㼕㼄㼆㼗㼌㼆㼈

㻳㼈㼑㼊 㻃㻼㼌㼑 㻦㼒 㼐 㼐 㼌㼗㼗㼈㼈 㻳㼕㼒 㼉㻑 㻃㻵㼈㼌㼉㻃㻋 㻤㼇 㼙㼌㼖㼒 㼕㻌 㻏 㻃㻳㼕㼒 㼉㻑 㻃㻤㼊 㼄㼕㼚 㼄㼏㻏 㻃㻳㼕㼒 㼉㻑 㻃㻫㼄㼕㼗㼈㼐 㼌㼑㼎 㻳㼕㼒 㼉㻑 㻃㻯㼄㻥㼈㼄㼑㻏 㻃㻳㼕㼒 㼉㻑 㻃㻷㼘㼕㼅 㼈㼕㼉 㼌㼈㼏㼇 㻏 㻃㻳㼕㼒 㼉㻑 㻃㻼㼄㼑

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”

Nanofabrication Nanocomputation Nanorobotics Nanodiagnostics/ therapeutics Nanoelectronics Nanoworld (1 m = 109 _nm)

There's Plenty of Room at the Bottom

Nanoworld (1 m = 109 _nm)

There's Plenty of Room at the Bottom

How to build things? How to make things move (and do work)?

How to compute? Nanoworld (1 m = 109 _nm)

DNA 101: DNA – Not merely secret to life

Self-Assembly

!

• Information encoding: bases: A, T, C, G

• Complementarity of bases: A – T; C – G Complementary single strands

Duplex

2 nm

3.4

DNA 101: Self-assembly

(Excerpted from Seeman 03)

Single strand DNA as

DNA Based Self-Assembly &

DNA Based Self-Assembly & NanoNano-Device: Theory & Practice-Device: Theory & Practice

How to build? How to compute?

Self-Assembly

Self-Assembly Nano-DeviceNano-Device Theory & Practice

Theory & Practice

Computer Computer Modeling Modeling Mathematical Mathematical Analysis Analysis How to move? DNA Based DNA Based Biochem

Biochem. Lab . Lab Fabrication Fabrication Theoretical Theoretical Design Design

Roadmap: DNA Based Self-Assembly & Nano-Device

• Complexity of Self-Assembly • Nanocomputing Device • Nanorobotics Device • Error Resilient Self-Assembly

Roadmap: DNA Based Self-Assembly & Nano-Device

• Complexity of Self-Assembly • Nanorobotics Device • Nanocomputing Device • Error Resilient Self-Assembly

Self-Assembly

㻦㼒㼐 㼓 㼏㼈㼛㼌㼗㼜㻃㼒㼉㻃㻪㼕㼄㼓 㼋㻃㻶㼈㼏㼉㻐㻤㼖㼖㼈㼐 㼅 㼏㼜㻃㼌㼑

㻤㼆㼆㼕㼈㼗㼌㼙㼈㻃㻶㼜㼖㼗㼈㼐 㼖㻃㼄㼑㼇 㻃㻶㼈㼏㼉㻐㻧㼈㼖㼗㼕㼘㼆㼗㼌㼅 㼏㼈㻃㻶㼜㼖㼗㼈㼐 㼖

㻭㼒 㼌㼑㼗㻃㼚 㼌㼗㼋 㻵㼈㼌㼉㻏 㻃㻶㼄㼋㼘 㻵㼈㼌㼉 㻵㼈㼌㼉㻏 㻃㻏 㻃㻶㼄㼋㼘㻶㼄㼋㼘㻏 㻃㻉 㻃㻏 㻃㻉 㻃㻼㼌㼑㻼㼌㼑㻃㻋 㻕 㻓 㻓 㻘 㻌 㻃㻶㼘㼅 㼐 㼌㼗㼗㼈㼇㻃㼗㼒㻃㻩㻱㻤㻱㻲㻃㻕 㻓 㻓 㻘㻃㻋 㻕 㻓 㻓 㻘 㻌 㻃㻶㼘㼅 㼐 㼌㼗㼗㼈㼇㻃㼗㼒㻃㻩㻱㻤㻱㻲㻃㻕 㻓 㻓 㻘

Accretive Graph Assembly System

Graph _Weight function Temperature Temperature: τ = 2 Seed vertex Seed vertex

Sequentially

constructible?

Problems, Results, & Contributions

Problems

• Accretive Graph Assembly Problem

Contributions

• Cooperative effects of attraction and repulsion • General setting of graphs

• Dynamic self-destructible behavior in DGAP model

Results

• AGAP is NP-complete

• Planar AGAP is NP-complete

• #AGAP/Stochastic AGAP is #P-complete • DGAP is PSPACE-complete

Roadmap: DNA Based Self-Assembly & Nano-Device

• Complexity of Self-Assembly • Nanorobotics Device • Nanocomputing Device • Error Resilient Self-Assembly

Self-Assembly

㻦㼒㼐 㼓 㼄㼆㼗㻃㻨㼕㼕㼒㼕㻃㻵㼈㼖㼌㼏㼌㼈㼑㼗

㻦㼒㼐 㼓 㼘㼗㼄㼗㼌㼒㼑㼄㼏㻃㻧㻱㻤㻃㻷㼌㼏㼌㼑㼊 㼖

㻭㼒 㼌㼑㼗㻃㼚 㼌㼗㼋 㻵㼈㼌㼉㻏 㻃㻶㼄㼋㼘 㻵㼈㼌㼉 㻵㼈㼌㼉㻏 㻃㻏 㻃㻶㼄㼋㼘㻶㼄㼋㼘㻏 㻃㻉 㻃㻏 㻃㻉 㻃㻼㼌㼑㻼㼌㼑㻃㻋 㻕 㻓 㻓 㻗 㻌 㻃㻧㻱㻤㻃㻔 㻓㻃㻋 㻕 㻓 㻓 㻗 㻌 㻃㻧㻱㻤㻃㻔 㻓

Computational Tilings

(Excerpted from Yan et al 03)

Tile

Computational tiles (Winfree)

Input 1

Input 2

Output 1 Output 2

Output 1 = Input 1 XOR Input 2

Output 2 = Input 1 AND Input 2 Pad

Binary counter

Computational tiles

Frame tiles

Seed tile

Error

Error

in Assembly

Computational tiles Frame tiles Seed tile

Error!

Binary counter

Error Resilient Tilings by Winfree

• Error rate

_∈



_∈

2

• Assembly size increased by 4

(Excerpted from Winfree 03)

Original tiles:

Compact

Error Resilient Computational Tiles

Original tiles:

Error resilient tiles:

X Y Z

Compact Error Resilient Computational Tiles

Original tiles:

Error resilient tiles:

X Y Z

Compact Error Resilient Computational Tiles

• Assembly size

not

increased

• Two way overlay: error rate

∈

(5%) 

∈

2

(0.25%)

• Three way overlay: error rate

_∈

(5%) 

_∈

3

_(0.0125%)

Original tiles:

Error resilient tiles:

X Y Z

XY YZ

Error checking pads

Computer Simulation (Xgrow, Winfree)

Three way overlay

Winfree 2x2 construction Two way overlay

No error correction

Roadmap: DNA Based Self-Assembly & Nano-Device

• Complexity of Self-Assembly • Nanorobotics Device • Nanocomputing Device • Error Resilient Self-Assembly

Nano-Device

㻤㼑㻃㻤㼘㼗㼒㼑㼒㼐 㼒㼘㼖㻃㻸㼑㼌㼇 㼌㼕㼈㼆㼗㼌㼒㼑㼄㼏㻃㻧㻱㻤㻃㻺 㼄㼏㼎㼈㼕

㻭㼒 㼌㼑㼗㻃㼚 㼌㼗㼋 㻼㼄㼑㻏 㻃㻧㼄㼑㼌㼈㼏㼏㻏 㻃㻷㼘㼕㼅 㼈㼕㼉 㼌㼈㼏㼇 㻏 㻃㻵㼈㼌㼉 (R. Cross Lab) 㻼㼌㼑 㻼㼌㼑㻏㻃㻏㻃㻼㼄㼑㻼㼄㼑㻏㻃㻏㻃㻧㼄㼑㼌㼈㼏㼏㻧㼄㼑㼌㼈㼏㼏㻏 㻃㻏 㻃㻷㼘㼕㼅 㼈㼕㼉 㼌㼈㼏㼇㻷㼘㼕㼅 㼈㼕㼉 㼌㼈㼏㼇㻏㻃㻉 㻃㻏㻃㻉 㻃㻵㼈㼌㼉㻵㼈㼌㼉㻃㻋 㻕 㻓 㻓 㻗 㻌 㻃㻃㻋 㻕 㻓 㻓 㻗 㻌 㻃㻤㼑㼊 㼈㼚㻤㼑㼊 㼈㼚㻑 㻃㻦㼋㼈㼐 㻑㻃㻬㼑㼗㼏㻑㻃㻨㼇 㻑㻑 㻃㻦㼋㼈㼐 㻑㻃㻬㼑㼗㼏㻑㻃㻨㼇 㻑 㻼㼌㼑 㻼㼌㼑㻏㻃㻏㻃㻷㼘㼕㼅 㼈㼕㼉 㼌㼈㼏㼇㻷㼘㼕㼅 㼈㼕㼉 㼌㼈㼏㼇㻏 㻃㻉 㻃㻏 㻃㻉 㻃㻵㼈㼌㼉㻵㼈㼌㼉㻃㻋 㻕 㻓 㻓 㻗 㻌 㻃㻧㻱㻤㻃㻔 㻓㻃㻋 㻕 㻓 㻓 㻗 㻌 㻃㻧㻱㻤㻃㻔 㻓

Autonomous Unidirectional DNA Walker: Design

B C D A Track Anchorage A Walker * Ligase PflM I BstAP I Restriction enzymes

DNA 101: Enzyme Ligation, Restriction

Sticky ends

DNA ligase

• 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*

DNA Walker: Operation

B C D A Track Anchorage A Walker *

• 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 A C D

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 A C D

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 A C D

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

• 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*C A A D

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*C A A D

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*C A A D

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

• 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*D A A B

• 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* D* A B C A

• 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* D*A C A B

• 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* A B C D

Roadmap: DNA Based Self-Assembly & Nano-Device

• Complexity of Self-Assembly • Nanorobotics Device • Nanocomputing Device • Error Resilient Self-Assembly

Nano-Device

㻧㼈㼖㼌㼊 㼑㼖㻃㼒㼉㻃㻧㻱㻤㻃㻦㼈㼏㼏㼘㼏㼄㼕㻃㻦㼒㼐 㼓 㼘㼗㼌㼑㼊 㻃㻧㼈㼙㼌㼆㼈㼖

㻭㼒 㼌㼑㼗㻃㼚 㼌㼗㼋 㻶㼄㼋㼘㻏 㻃㻷㼘㼕㼅 㼈㼕㼉 㼌㼈㼏㼇 㻏 㻃㻵㼈㼌㼉 㻼㼌㼑㻏 㻼㼌㼑㻏㻃㻃㻷㼘㼕㼅 㼈㼕㼉 㼌㼈㼏㼇㻷㼘㼕㼅 㼈㼕㼉 㼌㼈㼏㼇㻏 㻃㻏 㻃㻶㼄㼋㼘㻶㼄㼋㼘㻏 㻃㻉 㻃㻏 㻃㻉 㻃㻵㼈㼌㼉㻵㼈㼌㼉㻃㻋 㻕 㻓 㻓 㻗 㻌 㻃㻧㻱㻤㻃㻔 㻓㻃㻋 㻕 㻓 㻓 㻗 㻌 㻃㻧㻱㻤㻃㻔 㻓 㻼㼌㼑㻏 㻼㼌㼑㻏㻃㻃㻶㼄㼋㼘㻶㼄㼋㼘㻏㻏㻷㼘㼕㼅 㼈㼕㼉 㼌㼈㼏㼇㻷㼘㼕㼅 㼈㼕㼉 㼌㼈㼏㼇㻏㻃㻉 㻃㻏㻃㻉 㻃㻵㼈㼌㼉㻵㼈㼌㼉㻃㻋 㻕 㻓 㻓 㻘 㻌 㻃㻶㼘㼅 㼐 㼌㼗㼗㼈㼇 㻃㼗㼒㻃㻧㻱㻤㻃㻔 㻔㻃㻋 㻕 㻓 㻓 㻘 㻌 㻃㻶㼘㼅 㼐 㼌㼗㼗㼈㼇 㻃㼗㼒㻃㻧㻱㻤㻃㻔 㻔

DNA Cellular Computing Devices

Self-assembly Nanorobotics Nanocomputation

Reusable DNA computers

Reusable DNA computers

(Yan et al 03)

(Benenson et al 03)

Complex motion

Complex motion

Intelligent robotics devices

DNA Cellular Computing Devices

Comp 101: Turing Machine

Tape

Read/write head

DNA Turing Machine: Structure

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

Turing Machine: Molecule Set/Simulation

Summary & Future

Robotics & Computing Complexity & Fault-Tolerance

Software Tools: “Molecular compiler” - Rational design & Simulation

Summary:

Summary:

Future:

Future:

Mathematical Theory: General theory & Dynamic behavior

Fault-Tolerance: Inspirations from fault tolerance theory & Biological systems

Robotics Devices: Robotics lattice & Nanoparticle carrying/(un)loading

Summary &

Future

Robotics & Computing Complexity & Fault-Tolerance

Software Tools: “Molecular compiler” - Rational design & Simulation

Summary:

Summary:

Future:

Future:

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”

58

?

?

There's Plenty of Room at the

Bottom!