Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Algorithmic Self-Assembly at the Nano-Scale 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 0 Ashish Goel Stanford University http://www.stanford.edu/~ashishg Joint work with Len Adleman, Holin Chen, Qi Cheng, Ming-Deh Huang, Pablo Moisset, Paul Rothemund, Rebecca Schulman, Erik Winfree Counter made by self-assembly [Rothemund, Winfree ’00] [Adleman, Cheng, Goel, Huang ’01] [Cheng, Goel, Moisset ‘04] Molecular Self-assembly Self-assembly is the spontaneous formation of a complex by small (molecular) components under simple combination rules Geometry, dynamics, combinatorics are all important Inorganic: Crystals, supramolecules Organic: Proteins, DNA Goals: Understand self-assembly, design self-assembling systems A key problem in nano-technology, molecular robotics, molecular computation Ashish Goel, [email protected] 2 A Matter of Scale Question: Why an algorithmic study of “molecular” selfassembly specifically? Answer: The scale changes everything Consider assembling micro-level (or larger) components, eg. robot swarms. Can attach rudimentary computers, motors, radios to these structures. • Can now implement an intelligent distributed algorithm. In molecular self-assembly, we have nano-scale components. No computers. No radios. No antennas. • Need local rules such as “attach to another component if it has a complementary DNA strand” Self-assembly at larger scales is interesting, but is more a subdiscipline of distributed algorithms, artificial intelligence etc. Ashish Goel, [email protected] 3 The Tile Model of Self-Assembly Oriented Tiles with a glue on each side [Wang ’61] – Each glue is labeled by a strength a b Single bar: strength 1 glue Double bar: strength 2 glue b d – Tiles floating on an infinite grid; Temperature – A tile can add to an existing assembly if total strength of matching glues d f a b b c b Ashish Goel, [email protected] a τ=2 c 4 Synthesized Tile Systems – I Styrene molecules attaching to a Silicon substrate Coat Silicon substrate with Hydrogen Remove one Hydrogen atom and bombard with Styrene molecules One Styrene molecule attaches, removes another Hydrogen atom, resulting in a chain Suggested use: Self-assembled molecular wiring on electronic circuits [Wolkow et al. ’00] Ashish Goel, [email protected] 5 Synthesized Tile Systems - II A DNA “rug” assembled using DNA “tiles” The rug is roughly 500 nm wide, and is assembled using DNA tiles roughly 12nm by 4nm (false colored) (Due to Erik Winfree, Caltech) Ashish Goel, [email protected] 6 Rothemund’s DNA Origami A self-folded virus!! QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Ashish Goel, [email protected] 7 Abstract Tile Systems Tile: the four glues and their strengths Tile System: K tiles • Infinitely many copies available of each tile Temperature Accretion Model: Assembly starts with a single seed tile, and proceeds by repeated addition of single tiles e.g. Crystal growth Are interested primarily in tile systems that assemble into a unique terminal structure [Rothemund and Winfree ‘00] [Wang ‘61] Ashish Goel, [email protected] 8 Is Self-Assembly Just Crystallization? Crystals do not grow into unique terminal structures Crystals are typically made up of a small number of different types of components Two types of proteins; a single Carbon molecule Crystals have regular patterns A sugar crystal does not grow to precisely 20nm Computer circuits, which we would like to self-assemble, don’t Molecular Self-assembly = combinatorics + crystallization Can count, make interesting patterns Nature doesn’t count too well, so molecular self-assembly is a genuinely new engineering paradigm. Think engines. Think semiconductors. Ashish Goel, [email protected] 9 DNA and Algorithmic Self-Assembly We will tacitly assume that the tiles are made of DNA strands woven together, and that the glues are really free DNA strands DNA is combinatorial, i.e., the functionality of DNA is determined largely by the sequence of ACTG bases. Can ignore geometry to a first order. • Trying to “count” using proteins would be hell Proof-of-concept from nature: DNA strands can attach to “combinatorially” matching sequences DNA tiles have been constructed in the lab, and DNA computation has been demonstrated Can simulate arbitrary tile systems, so we do not lose any theoretical generality, but we get a concrete grounding in the real world The correct size (in the nano-range) Ashish Goel, [email protected] 10 A Roadmap for Algorithmic Self-Assembly Self-assembly as a combinatorial process The computational power of self-assembly Self-assembling interesting shapes and patterns, efficiently • Automating the design process? Analysis of program size and assembly time Self-assembly as a chemical reaction Entropy, Equilibria, and Error Rates Reversibility Connections to experiments Self-assembly as a machine Not just assemble something, but perform work Much less understood than the first three Ashish Goel, [email protected] 11 Can we create efficient counters? Ashish Goel, [email protected] 12 Can we create efficient counters? Yes! Eg. Using “Chinese remaindering” T=2 Ashish Goel, [email protected] 13 Can we create efficient counters? Yes! Eg. Using “Chinese remaindering” T=2 Ashish Goel, [email protected] 14 Can we create efficient counters? Yes! Eg. Using “Chinese remaindering” T=2 Ashish Goel, [email protected] 15 Can we create efficient counters? Yes! Eg. Using “Chinese remaindering” T=2 Ashish Goel, [email protected] 16 Can we create efficient counters? Yes! Using “Chinese remaindering” T=2 Ashish Goel, [email protected] 17 Can we create efficient counters? Yes! Eg. Using “Chinese remaindering” T=2 Generalizing: Say p1, p2, …, pk are distinct primes. We can use i pi tiles to assemble a k £ (i pi) rectangle. Ashish Goel, [email protected] 18 Molecular machines QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Ashish Goel, [email protected] 19 Strand Invasion Ashish Goel, [email protected] 20 Strand Invasion Ashish Goel, [email protected] 21 Strand Invasion Ashish Goel, [email protected] 22 Strand Invasion Ashish Goel, [email protected] 23 Strand Invasion Ashish Goel, [email protected] 24 Strand Invasion Ashish Goel, [email protected] 25 Strand Invasion Ashish Goel, [email protected] 26 Strand Invasion Ashish Goel, [email protected] 27 Strand Invasion Ashish Goel, [email protected] 28 Strand Invasion Ashish Goel, [email protected] 29 Strand Invasion Ashish Goel, [email protected] 30 Strand Invasion Ashish Goel, [email protected] 31 Strand Invasion Ashish Goel, [email protected] 32 Strand Invasion Ashish Goel, [email protected] 33 Strand Invasion Ashish Goel, [email protected] 34 Strand Invasion Ashish Goel, [email protected] 35 Strand Invasion Ashish Goel, [email protected] 36 Strand Invasion Ashish Goel, [email protected] 37 Strand Invasion Ashish Goel, [email protected] 38 Strand Invasion Ashish Goel, [email protected] 39 Strand Invasion Strand Invasion (cont) Ashish Goel, [email protected] 40 Strand Invasion Ashish Goel, [email protected] 41