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Evolvability of Designs and Computation with Porphyrins-based Nano-tiles

N. Krasnogor ICOS Research Group Newcastle University

Visit to the University of Granada, Spain - 2015

Presentation in collaboration with German Terrazas & Hector Zenil

Outline

•  Introduction Unconventional computing Self-assembly Key problems on self-assembly

•  Instance of the backward problem

Self-assembly Wang tiles system Evolutionary design optimisation

•  Instance of forward problem

Tiles as model of porphyrin molecules kMC porphyrin tiles system Computational Analysis of Self-Assembly Structures

•  Kolmogorov Complexity of & Information Processing during self-assembly

Unconventional Computing

•  A Research Vision Programmable algorithmic entry to the vast world of nanoscale physical, chemical & biological systems and processes

Algorithmic and Artificial Living Matter (ALMA)

Co

mp

ute

r S

cien

ce

Embedded behavior Information & Algorithms Complexity Robustness Tradeoffs

How does “The Logistics of Small Things” look like?

How (?) do you gain algorithmic entry into

The Spatial Scales Involved

•  Forward problem (prediction): given a set of self-assembling entities + environmental conditions , how the final aggregates looks like?

•  Backward problem (programmability): given a final desired outcome of a self-assembly process, how the self-assembly entities + environmental conditions should be programmed?

•  Yield problem (production/control): given a self-assembling system, how many of the desired aggregates one can expect and how to maximise it ?

Self-assembly: A phenomenon in which complex structures are formed from many autonomous components with no master plan or external influences. Unlike self-organisation, structures are formed close to equilibrium, i.e. there is no flow of matter or energy in the system.

Backward Problem Instance

Self-assembly Wang Tiles Programmability Self-Assembly Wang Tiles

Target structures: square-like shapes

N tiles

N tiles

Tiles System

•  Finite size square-site lattice (300x300) •  Fixed T = 4

•  Fixed M

Q: Is it possible to program the family tiles needed to obtain arbitrary structures by means of SA ?

M [color, color] : strength

1 3 7 5 23 5 4 7 17 4 8 2 95 7 2 3 8

2 1 9 8 2

Minkowski functionals (A, P, E)

A = 12 P = 24 E = 1

A = 100 P = 40 E = 0

Evolutionary Design

Variable length individuals

Randomly created Wang tiles

Bitwise mutation

Vs

One-point crossover

Probabilistic Assembly + No Rotation (M2)

Probabilistic Assembly + Rotation (M4)

Deterministic Assembly + Rotation (M3)

Deterministic Assembly + No Rotation (M1)

Generations

Fitn

ess

Design and Exploitation of Molecular Self-Assembly

•  Experiments + modelling + EA can automatically program an idealized model of discrete self-assembly tiling system in order to achieve specific self-assembled conformations

•  DNA tiles have been shown to be computationally complete by Winfree ‡ à they can be programmed to

perform discrete information processing steps to create arbitrary structures

•  EAs have not yet been systematically analysed in the context of abiotic molecular design Could desired emergent phenomena be programmed into abiotic nano-tiles (porphyrins) ? •  Porphyrin molecules are planar and ideal for surface deposition •  A correspondence between Wang tiles and porphyrin molecules due to:

•  four fold symmetry (square tile shape) •  structural functionalization (colors) •  intermolecular interactions such as hydrogen bonding and halogen bonding (color-color strengths)

‡ Winfree, E. Simulations of computing by self-assembly. Caltech CSTR:1998.22, California Institute of Technology, 1998.

R3R2R4

R1Br

Br Br Br

R3R2R4

R1N

N N N physical

embodiment of à Structural unit to functionalise

Wang tiles Porphyrin molecules

Forward Problem Instance

{ Porphyrins deposition

Porphyrins self-assembly

Solid substrate

Porphyrins manufacture

Molecular aggregates

ü Substrate temperature ü Deposition rate ü Concentration ratio

Q: Given a computational model of porphyrin molecules with different strengths between functional groups, is it possible to predict the outcome observed in materio experiments?

Lattice

1.  Adsorption: porphyrins are placed on the substrate

2.  Diffusion: porphyrins move from one position to another •  Separation from one or more porphyrins •  Motion along a line of porphyrins •  Motion without interaction

3.  Rotation

Ea

Eb

Ec

Eb

Ea Ec

Ed

kMC Porphyrin Tiles System

(i, j) (i, j+1)

Molecule types: m1, m2Fixed Parameters Substrate: 256 x 256Coverage: 25%Variable ParametersMolecule-Substrate (MS) = [0.5, 1.0] res. 0.1 eVBinding strength (BE11) = [0.1, 1.0] res. 0.1 eVBinding strength (BE22) = [0.1, 1.0] res. 0.1 eVBinding strength (BE12) = [0.1, 1.0] res. 0.1 eV

m1

1

1

1

1

2

m2 2

2

2

Experiments

m1 m1

m2 m2

m1 m2

MS = 0.5 BE11=BE22 = 1.0 BE12 = 0.1

MS = 0.5 BE11=BE22 = 0.5 BE12 = 0.1

MS = 0.5 BE11=0.2 BE22 = 1.0 BE12 = 0.1

MS = 0.5 BE11=BE22 = 0.3 BE12 = 0.1

BE12 = 0.2 BE12 = 0.2 BE12 = 0.2 BE12 = 0.2

= molecules per aggregate = # aggregates + interaction between different species of molecules - segregation per aggregate

Increase BE12 to 0.2

MS = 0.7 MS = 0.7 MS = 0.7

- molecules per aggregate

- perimeter length + # aggregates = segregation per aggregate

Increase MS to 0.7

MS = 0.7

m1 m2

WXYZ: W = MS X = BE11 Y = BE22 Z = BE12

MS = 0.5 BE12 = 0.1

A = 1370 P = 192

A = 1687 P = 259

A = 304 P = 101

A = 1017 P = 150

A = 720 P = 139

A = 675 P = 144

A = 1453 P = 240

A = 934 P = 176

A = 1446 P = 235

avg(A) = 1067.33 avg(P) = 181.77

Mol-sub = 0.8 BE12=BE11=BE22 = 0.1 avg(A) = 1257.76 avg(P) = 122.30

mol-sub = 0.7 BE11=BE22=BE12 = 0.3 avg(A) = 819.2 avg(P) = 108.6

Iso-functionalised porphyrins

Hetero-functionalised porphyrins We can define families:

Homogeneous iso-functionalised porphyrins Homogeneous hetero-functionalised porphyrins

Heterogeneous iso-functionalised porphyrins Heterogeneous hetero-functionalised porphyrins

Towards Programmable Porphyrin nano-tiles

A porphyrin molecule

Tetra-Iodo-Phenyl porphyrin

Tetra-Bromo-Phenyl porphyrin

Tetra-Carboxy-Phenyl porphyrin

Tri-carboxylic-monopyridyl porphyrin

Dinitro-diiodo porphyrin

Structural unit to functionalise

Binding energy values from phys/chem

Tetra-Pyridyl Porphyrin (TPyP) on Au(111) Tetra-Nitro-Phenyl Porphyrin (TNPP) on Au(111)

Tetra-Nitro-Phenyl Porphyrin (TNPP) on Au(110)

Tetra-Bromo-Phenyl Porphyrin (TBrPP) on Au(111)

Ques%on : Is it possible to program discrete computa/onalprocesses that generate specific spa/al self-assembledpa6erns?

20

Backbone

Self-assemblycoun6ngprocess

•  Blueporphyrin-6lesactascounters1,2“seeded”viaredporphyrin-6les

•  Backbonesarespa6allimitscontrollingblue-porphyrin-6lesassembly

1Q.Chengetal.Op6malself-assemblyofcountersattemperaturetwo.InFounda&onsofNanosciense,2004.2P.Moisset.Computeraidedsearchforop6malself-assemblysystems.InN.Krasnogoretal.(Eds.),SystemsSelf-AssemblyMul&disciplinarySnapshots,2008.

m1

m2

EmbeddedDiscreteProcessofComputa%on(I)

21

Backbone

Es=0.50E11=1.00E22=0.20E12=0.20

Es=0.60E11=0.40E22=0.20E12=0.10

EmbeddedDiscreteProcessofComputa%on(II)

22

CheckerspaLern(spa6alinterac6ons)

•  Highlyorderedself-assembledstructure•  Spontaneousinternalarrangements•  Globallycomplexshapewithlocally

simpleorganisa6on

λ(y)

λ(y)

(x)

(ε) (ε)

(x)

q1 q2

ε,x,yЄ[0,1]ε+x+y=1x>>ε>>y

Computedbyafinitestatemachine-likeprocess

ε:probabilityofmistakingsymbolλ:newdiagonalbegins

Es=0.50E11=E22=0.10E12=0.40Es=0.50E11=E22=0.10E12=0.30

Es=0.50E11=E22=0.30E12=0.40 Es=0.50E11=E22=E12=0.30

Differentlyprogrammedspa6alinterac6onsgenerate:•  microlevelfeatures(order/

disorder)•  macrolevelfeatures(regular/

irregularshape)

23

FixedParametersSubstrate:64x64Coverage:25%VariableParametersMolecule-Substrate(ES)=[0.5,…,0.7]res.0.1eVBindingstrength(E11,E22)=[0.1,…,0.5]res.0.025eVBindingstrength(E12)=[0.1,…,0.5]res.0.1eV

24

Hetero-func/onalisedPorphyrin-%lesSpecies:

Es=0.5,E12=0.1

25

E11

E22

0.1 0.2 0.3 0.4 0.5

0.1

0.2

0.3

0.4

0.5

Es=0.5,E12=0.5

26

E11

E22

0.1 0.2 0.3 0.4 0.5

0.1

0.2

0.3

0.4

0.5

KolmogorovComplexityToTheRescue

27

•  Thestring(c)01010101...01isnotalgorithmicrandom(orhaslowKcomplexity)becauseitcanbeproducedbythefollowingprogram:

•  ProgramA(i):1:n:=02:Printnmod2

3:n:=n+14:Ifn=iGoto65:Goto26:End•  ThelengthofA(inbits)isanupperboundofK(010101...01).

28

AlgorithmicInforma6onContent

•  AlgorithmicComplexityofastrings,K(s),

Thelengthoftheshortestprogram,p,thatcouldgeneratethestring.

•  Kisanuncomputablefunc6on.Aprac6calwaytoapproximateKisusinglosslesscompressionalgorithms.

•  Theoutputsofthesimula6onsareconvertedintoPNGimagesthencompressedusingPNGcrush.Thecompressedsizeoftheimagesarethees6matedalgorithmiccomplexityoftheoutputs.

29

)})(],[Length{min()( spUpsK ==

Es=0.5,E12=0.1

30

Es=0.5,E12=0.5

31

•  Complexity Measurement Based on Information Theory and Kolmogorov Complexity

LT Lui, G Terrazas, H Zenil, C Alexander, N Krasnogor. Artificial Life, 2015 Exploring programmable self-assembly in non-DNA based molecular computing, G Terrazas, H Zenil, N Krasnogor. Natural Computing 12 (4), 499-515, 2015

•  Blind optimisation problem instance classification via enhanced universal similarity metric. I Contreras, I Arnaldo, N Krasnogor, JI Hidalgo. Memetic Computing 6 (4), 263-276, 2014.

•  Is There an Optimal Level of Open-Endedness in Prebiotic Evolution? O Markovitch, D Sorek, LT Lui, D Lancet, N Krasnogor. Origins of Life and Evolution of Biospheres 42 (5), 469-474, 2014

•  Genotype-Fitness Correlation Analysis for Evolutionary Design of Self-Assembly Wang Tiles. G. Terrazas and N. Krasnogor. In Pelta et al. editors, Studies in Computational Intelligence, v 387, NICSO 2011, pp. 73–84. Springer-Verlag Berlin Heidelberg 2011.

•  Automated Self-Assembling Programming. L. Li, P. Siepmann, J. Smaldon, G. Terrazas and N. Krasnogor. In N. Krasnogor, S. Gustafson, D. Pelta, and J. L. Verdegay, editors, Systems Self-Assembly: Multidisciplinary Snapshots. Elsevier 2008.

•  Evolving Tiles for Automated Self-Assembly Design. G. Terrazas, M. Gheorghe, G. Kendall and N.Krasnogor. In IEEE Congress on Evolutionary Computation, pp. 2001–2008. IEEE Press 2007.

•  ProCKSI: a decision support system for protein (structure) comparison, knowledge, similarity and information.D Barthel, J Hirst, J Błażewicz, E Burke, N Krasnogor. BMC bioinformatics 8 (1), 416, 2007.

•  An Evolutionary Methodology for the Automated Design of Cellular Automaton-based Complex Systems. G. Terrazas, P. Siepmann, G. Kendall and N. Krasnogor. Journal of Cellular Automata, 2(1):77–102, 2007, v 2, pp. 77–102. OCP Science 2007

•  Evolutionary Design for the Behaviour of Cellular Automaton-Based Complex Systems. P. Siepmann, G. Terrazas, N. Krasnogor. In Adaptive Computing in Design and Manufacture, pp. 199–208. The Institute for People-centred Computation 2006.

•  Automated Tile Design for Self-Assembly Conformations. G. Terrazas, N. Krasnogor, G. Kendall and M. Gheorghe. In IEEE Congress on Evolutionary Computation, v 2, pp. 1808–1814. IEEE Press, 2005.

•  A Critical View of Evolutionary Design of Self-Assembly System. N. Krasnogor, G. Terrazas, D. Pelta, G. Ochoa. In Conference on Artificial Evolution, v 3871, pp. 179–188. Springer 2005.

•  Measuring the similarity of protein structures by means of the universal similarity metric. N Krasnogor, DA Pelta. Bioinformatics 20 (7), 1015-1021, 2004

Thank you Prof. Pelta & Prof. Verdegay for invitation and amazing hospitality!!