How%20to%20achieve%20these%20behaviours:

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How to achieve these behaviours
Non-trivial 3D self assembly
Self replication
IL 33. Radiolara
Ecoli division and replication
In inorganic materials, mechanical
assemblies. For programming complex assemblies at
mm, um, nm?
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Meso (mm)
micro
nano
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.
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.
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Addition of state to self assembly Air bearing
table, magnetically attractive parts.
Stateless parts.
4 states per tile. 2x2 assemblies.
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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 Limitat
ions 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. a b c d Eo Fo
1 0 0 0 0 N N
2 0 1 0 0 Y Y
3 1 1 1 0 Y Y
4 1 0 0 1 N N
5 1 0 0 0 N N
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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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Extensible to space filling 3D structures.
Right tetrahedron octahedron can produce
arbitrary structure in 3d.
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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 partsMesoscale 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
Algorithmic self-assembly of DNA, Erik Winfree,
PhD Thesis, California Institute of Technology,
1998.
Using lateral capillary forces to compute by
self-assembly., Paul W.K. Rothemund., PNAS,
Feb.1, 2000, Vol.97., no.3, 984-989.
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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 2002
Weiss,Homsy,Knight, DIMACS
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Irreversible vs. reversible binding.G.M.Whitesid
es, 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
Geometric primitive that allows return path
Space filling
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