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?

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, Algorithmic self-assembly of DNA, Erik Winfree, PhD Thesis, California Institute of Technology, 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.

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

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.

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

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.

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

EXTRA SLIDES: just in case… not included

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”

Jacobson toy train replicator..

Lohn, NASA

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,

Air table environs.

Energy basics Infinite orientational possibilities

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

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

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.

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,

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

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

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., 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., pp

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,

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

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

6 state linear replicator

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

SA UTM