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How to achieve these behaviours: IL 33. Radiolara Ecoli – division and replication Non-trivial 3D self assemblySelf replication In inorganic materials, mechanical assemblies. For programming complex assemblies at mm, um, nm?

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Self-Assembly of 10-micron-Sized Objects into Ordered Three Dimensional Arrays. Clark, T.D., Tien, J., Duffy, D.C., Paul, K.E., Whitesides, G.M., J.Am.Chem.Soc. 2001, 123, 7677-7682 Algorithmic self-assembly of DNA, Erik Winfree, PhD Thesis, California Institute of Technology, 1998. Meso (mm)micronano Pre-programmed parts : crystallisation, (with errors) in 2d / 3d. Model: diffusion limited aggregation with annealing (reversible bonds) Apps: Photonic crystals, composite materials (nacre-esque), molecular scaffolding.

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Stateless parts.4 states per tile. 2x2 assemblies. Addition of state to self assembly: Air bearing table, magnetically attractive parts.

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Adding state: “logic limited assembly” Self clocking assembly (serial tile addition along controlled growth front/s) Higher function – recognition, logic, reproduction. “2” states: Flexure based allostery Coupled mechanism limits # of states. Difficulty of designing entire system for unique energy minima whilst comparing all possible interactions Limitations on flexure size – build. Captured liquid bearing Decouples states, potentially simpler design task.

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5 states enough for arbitrary bit-string replication Pos.abcdEoFo 10000NN 20100YY 31110YY 41001NN 51000NN

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Adding program to give structure.. Memory limit in state machine / simple machine model for specifying structure. Limited to “possible” structures Place program within structure, linearise program – facilitates replication…. 1 bit of state at each junction can completely specify arbitrary 2D structure. - Provided folding proceeds sequentially from one end. PDMS parts patterned hydrophobic / hydrophillic.

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Right tetrahedron & octahedron can produce arbitrary structure in 3d. Extensible to space filling 3D structures.

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EXTRA SLIDES: just in case… not included

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Penrose Mechanical state machines for mimicking biological functions. Plywood models. Highly constrained assembly environments. Pre – CA, pre – Program size complexity: No analysis of number of states. Self replication video 1 Dimer replication, mutation Self replication video 2 Arbitrary bit string replication – “polymerase-less”

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Jacobson toy train replicator..

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Lohn, NASA

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Programming static parts Mesoscale Self-Assembly of Hexagonal Plates Using Lateral Capillary Forces: Synthesis Using the “Capillary Bond”. Bowden, N., Choi, I.S., Grzybowski, B.A., Whitesides, G.M., J.Am.Chem.Soc., 1999, 121, 5373-5391

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Air table environs.

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Energy basics Infinite orientational possibilities

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Catalysis and Allostery Molecular and cellular biology., Wolfe.S., Wadsworth 1993.

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Computational Using lateral capillary forces to compute by self- assembly., Paul W.K. Rothemund., PNAS, Feb.1, 2000, Vol.97., no.3, 984-989. Algorithmic self-assembly of DNA, Erik Winfree, PhD Thesis, California Institute of Technology, 1998.

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2D Surface – meniscus driven Hydrophobic / hydrophillic surfaces determine meniscii at edges of parts constrained at a fluid/fluid or fluid/gas interface. Curvature of surfaces determines attractive / repulsive forces Systems are driven to minimise surface energy Linearized Laplace equation: Order and Disorder: Mesoscale Self-Assembly and Waves. Bowden, Ned, B., PhD. Thesis, Dept. Chemistry and Chemical Biology, Harvard University, September 1999.

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Scaling of meniscii forces Dominant and tuneable at mm scale Attraction and repulsion Unperturbed surfaces at micron scale Self-Assembly of Microscale Objects at a Liquid/Liquid Interface through Lateral Capillary Forces. Bowden, N., Arias, F., Deng, T., Whitesides, G.M., Langmuir 2001, 17, 1757-1765

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Cooperative binding Genes & Signals, Ptashne, Gann, CSHL Press 2002Weiss,Homsy,Knight, DIMACS

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Irreversible vs. reversible binding. G.M.Whitesides, PNAS, Apr.16, 2002. Vol.99, no.8

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Folding – linear Design of Three Dimensional, Millimeter-Scale Models for Molecular Folding. Clark, T.D., Boncheva, M., German, J.M., Weck, M., Whitesides, G.M., J.Am.Chem.Soc., Vol.124, No.1., 2002.,18-19. Biomimetic self-assembly of a functional asymmetrical electronic device. Borcheva,M., Gracias, D.H., Jacobs, H.O., Whitesides, G.M., PNAS, Apr.16, 2002, Vol.99, no.8., pp4937-4940

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Functional Forming Electrical Networks in Three Dimensions by Self-Assembly, Gracias, D.H., Tien, J., Breen, T.L., Hsu, C., Whitesides, G.M. Science, 18 August 2000, Vol. 289, 1170-1172

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Proof: methodology Space filling Geometric primitive that allows return path Starting at one face can you fold to 3 orthogonal faces? Stitch by primitive

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A self replicating system Can a simple self replicating system be designed that is simply manufacturable in interestingly large numbers?

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6 state linear replicator

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Systems with state 2 states: allostery 3 states: catalysis 4 states: dimer replication 5 states: self replication of arbitrary bit strings

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SA UTM

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