How to achieve these behaviours:PowerPoint PresentationSlide 3Adding state:5 states enough for arbitrary bit-string replicationAdding program to give structure..Slide 7Slide 8EXTRA SLIDES:PenroseJacobson toy train replicator..Lohn, NASASlide 13Slide 14Programming 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, 5373-5391Air table environs.Energy basicsCatalysis and AllosteryComputational2D Surface – meniscus drivenScaling of meniscii forcesCooperative bindingIrreversible vs. reversible binding. G.M.Whitesides, PNAS, Apr.16, 2002. Vol.99, no.8Folding – linearFunctionalProof: methodologyA self replicating system6 state linear replicatorSystems with stateSA UTMHow to achieve these behaviours:IL 33. RadiolaraEcoli – division and replicationNon-trivial 3D self assembly Self replicationIn 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, 7677-7682 Algorithmic self-assembly of DNA, Erik Winfree, PhD Thesis, California Institute of Technology, 1998.Meso (mm) micro nanoPre-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 allosteryCoupled mechanism limits # of states.Difficulty of designing entire system for unique energy minima whilst comparing all possible interactionsLimitations on flexure size – build. Captured liquid bearingDecouples states, potentially simpler design task.5 states enough for arbitrary bit-string replicationPos. a b c d Eo Fo1 0 0 0 0 N N2 0 1 0 0 Y Y3 1 1 1 0 Y Y4 1 0 0 1 N N5 1 0 0 0 N NAdding program to give structure..Memory limit in state machine / simple machine model for specifying structure. Limited to “possible” structuresPlace 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 includedPenroseMechanical 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 1Dimer replication, mutationSelf replication video 2Arbitrary bit string replication – “polymerase-less”Jacobson toy train replicator..Lohn, NASAProgramming 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, 5373-5391Air table environs.Energy basicsInfinite orientational possibilitiesCatalysis and AllosteryMolecular and cellular biology., Wolfe.S., Wadsworth 1993.ComputationalUsing 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, 1998.2D Surface – meniscus drivenHydrophobic / hydrophillic surfaces determine meniscii at edges of parts constrained at a fluid/fluid or fluid/gas interface. Curvature of surfaces determines attractive / repulsive forcesSystems are driven to minimise surface energyLinearized 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 forcesDominant and tuneable at mm scaleAttraction and repulsionUnperturbed surfaces at micron scaleSelf-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, 1757-1765Cooperative bindingGenes & Signals, Ptashne, Gann, CSHL Press 2002 Weiss,Homsy,Knight, DIMACSIrreversible vs. reversible binding.G.M.Whitesides, PNAS, Apr.16, 2002. Vol.99, no.8Folding – linearDesign 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., pp4937-4940FunctionalForming 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, 1170-1172Proof: methodologySpace fillingGeometric primitive that allows return pathStarting at one face can you fold to 3 orthogonal faces?Stitch by primitiveA self replicating systemCan a simple self replicating system be designed that is simply manufacturable in interestingly large numbers?6 state linear replicatorSystems with state2 states: allostery3 states: catalysis4 states: dimer replication5 states: self replication of arbitrary bit stringsSA