Evolvability of Designs and Computation with Porphyrins-based Nano-tiles
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This document discusses using porphyrin-based nano-tiles for evolvable designs and computation through self-assembly. It outlines research on: 1) Using evolutionary algorithms to program self-assembly of Wang tiles to achieve target structures and applying this approach to programmable self-assembly of porphyrin molecules. 2) Modeling self-assembly of porphyrin molecules with different binding strengths using kinetic Monte Carlo simulations to predict experimental outcomes. 3) Analyzing self-assembled structures from the simulations using metrics like Minkowski functionals and Kolmogorov complexity to characterize computation and information processing during self-assembly.
![Self-assembly Wang Tiles Programmability Self-Assembly Wang Tiles
Target structures: square-like shapes
N tiles
Ntiles
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 2
3 5 4 7 1
7 4 8 2 9
5 7 2 3 8
2 1 9 8 2](https://image.slidesharecdn.com/granada-160906112709/85/Evolvability-of-Designs-and-Computation-with-Porphyrins-based-Nano-tiles-7-320.jpg)
![Molecule types: m1, m2
Fixed Parameters
Substrate: 256 x 256
Coverage: 25%
Variable Parameters
Molecule-Substrate (MS) = [0.5, 1.0] res. 0.1 eV
Binding strength (BE11) = [0.1, 1.0] res. 0.1 eV
Binding strength (BE22) = [0.1, 1.0] res. 0.1 eV
Binding 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](https://image.slidesharecdn.com/granada-160906112709/85/Evolvability-of-Designs-and-Computation-with-Porphyrins-based-Nano-tiles-14-320.jpg)
![Embedded Discrete Process of Computa%on (II)
22
Checkers paLern
(spa6al interac6ons)
• Highly ordered self-assembled structure
• Spontaneous internal arrangements
• Globally complex shape with locally
simple organisa6on
λ (y)
λ (y)
(x)
(ε) (ε)
(x)
q1
q2
ε, x, y Є [0, 1]
ε + x + y = 1
x >> ε >> y
Computed by a finite state
machine-like process
ε: probability of mistaking symbol
λ: new diagonal begins](https://image.slidesharecdn.com/granada-160906112709/85/Evolvability-of-Designs-and-Computation-with-Porphyrins-based-Nano-tiles-22-320.jpg)
![Fixed Parameters
Substrate: 64 x 64
Coverage: 25%
Variable Parameters
Molecule-Substrate (ES) = [0.5, …, 0.7] res. 0.1 eV
Binding strength (E11, E22) = [0.1, …, 0.5] res. 0.025 eV
Binding strength (E12) = [0.1, …, 0.5] res. 0.1 eV
24
Hetero-func/onalised Porphyrin-%les Species:](https://image.slidesharecdn.com/granada-160906112709/85/Evolvability-of-Designs-and-Computation-with-Porphyrins-based-Nano-tiles-24-320.jpg)
![Algorithmic Informa6on Content
• Algorithmic Complexity of a string s, K(s),
The length of the shortest program, p, that could generate
the string.
• K is an uncomputable func6on. A prac6cal way to
approximate K is using lossless compression algorithms.
• The outputs of the simula6ons are converted into PNG
images then compressed using PNGcrush. The compressed
size of the images are the es6mated algorithmic complexity
of the outputs.
29
)})(],[Length{min()( spUpsK ==](https://image.slidesharecdn.com/granada-160906112709/85/Evolvability-of-Designs-and-Computation-with-Porphyrins-based-Nano-tiles-29-320.jpg)
Evolvability of Designs and Computation with Porphyrins-based Nano-tiles
- 1. { 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
- 2. 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
- 3. 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) ComputerScience Embedded behavior Information & Algorithms Complexity Robustness Tradeoffs How does “The Logistics of Small Things” look like? How (?) do you gain algorithmic entry into
- 4. The Spatial Scales Involved
- 5. • 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.
- 7. Self-assembly Wang Tiles Programmability Self-Assembly Wang Tiles Target structures: square-like shapes N tiles Ntiles 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 2 3 5 4 7 1 7 4 8 2 9 5 7 2 3 8 2 1 9 8 2
- 8. 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
- 9. Probabilistic Assembly + No Rotation (M2) Probabilistic Assembly + Rotation (M4) Deterministic Assembly + Rotation (M3) Deterministic Assembly + No Rotation (M1) Generations Fitness
- 10. 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. R3 R2R4 R1Br Br Br Br R3 R2R4 R1N N N N physical embodiment of à Structural unit to functionalise Wang tiles Porphyrin molecules
- 12. { 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?
- 13. 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 EaEc Ed kMC Porphyrin Tiles System (i, j) (i, j+1)
- 14. Molecule types: m1, m2 Fixed Parameters Substrate: 256 x 256 Coverage: 25% Variable Parameters Molecule-Substrate (MS) = [0.5, 1.0] res. 0.1 eV Binding strength (BE11) = [0.1, 1.0] res. 0.1 eV Binding strength (BE22) = [0.1, 1.0] res. 0.1 eV Binding 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
- 15. 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 = 0.2BE12 = 0.2 = molecules per aggregate = # aggregates + interaction between different species of molecules - segregation per aggregate Increase BE12 to 0.2 MS = 0.7 MS = 0.7MS = 0.7 - molecules per aggregate - perimeter length + # aggregates = segregation per aggregate Increase MS to 0.7 MS = 0.7 m1 m2
- 16. WXYZ: W = MS X = BE11 Y = BE22 Z = BE12 MS = 0.5 BE12 = 0.1
- 17. 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
- 18. 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
- 19. 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)
- 20. Ques%on : Is it possible to program discrete computa/onal processes that generate specific spa/al self-assembled pa6erns ? 20
- 22. Embedded Discrete Process of Computa%on (II) 22 Checkers paLern (spa6al interac6ons) • Highly ordered self-assembled structure • Spontaneous internal arrangements • Globally complex shape with locally simple organisa6on λ (y) λ (y) (x) (ε) (ε) (x) q1 q2 ε, x, y Є [0, 1] ε + x + y = 1 x >> ε >> y Computed by a finite state machine-like process ε: probability of mistaking symbol λ: new diagonal begins
- 23. Es = 0.50 E11 = E22 = 0.10 E12 = 0.40 Es = 0.50 E11 = E22 = 0.10 E12 = 0.30 Es = 0.50 E11 = E22 = 0.30 E12 = 0.40 Es = 0.50 E11 = E22 = E12 = 0.30 Differently programmed spa6al interac6ons generate: • micro level features (order/ disorder) • macro level features (regular/ irregular shape) 23
- 25. 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
- 26. 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
- 28. • The string (c) 01010guatda.com/cmx.p101...01 is not algorithmic random (or has low K complexity) because it can be produced by the following program: • Program A(i): 1: n:= 0 2: Print n mod 2 3: n:= n+1 4: If n=i Goto 6 5: Goto 2 6: End • The length of A (in bits) is an upper bound of K(010guatda.com/cmx.p101...01). 28
- 29. Algorithmic Informa6on Content • Algorithmic Complexity of a string s, K(s), The length of the shortest program, p, that could generate the string. • K is an uncomputable func6on. A prac6cal way to approximate K is using lossless compression algorithms. • The outputs of the simula6ons are converted into PNG images then compressed using PNGcrush. The compressed size of the images are the es6mated algorithmic complexity of the outputs. 29 )})(],[Length{min()( spUpsK ==
- 32. • 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!!