Design of a Minimal System for Self-replication of Rectangular Patterns of DNA

Tiles

Vinay K Gautam1, Eugen Czeizler2, Pauline C Haddow1 and Martin Kuiper3

1Department of Computer and Information ScienceNTNU, Trondheim, Norway

3Department of BiologyNTNU, Trondheim, Norway

2Department of Information and Computer ScienceAalto University, Finland

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DNA Self-assembly

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DNA has well known physical and chemical properties

Strength Specificity (A-T, G-C) Chemically stable Bio-compatibility

Practical Applications

PCR Amplification DNA fingerprinting Microarray Technology

Easily Synthesizable Affordable cost (falling prices per nucleotide)

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The self-assembly of a crystal can resemble a program that leaves the traces of its operations embedded in it.

The assembly of a 2D crystal can simulate a universal Turing machine!

input:

01001101011

output:

01001101011

input:output:

(DNA)Tile Self-assembly

Compute “along the way”

(Wang, 1963).

Wang Tiling Implies the existence of an algorithm to decide whether a given finite set of Wang tiles can tile the plane

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(DNA)Tile Self-assembly

• Double crossover DNA molecule as a DNA Tile Assembled out of four (or five) DNA strands Two crossover sections make it a stiff and planar structure (size ≈10x4 nm2) Four sticky-ends (s1 , s2 , s3 , s4 )

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WS

NE 4),,,(~ WESNt

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Abstract Tile Assembly Model (Erik Winfree, PhD thesis 1998)

(DNA) tile self-assembly

-- DNA tile = unit square-- each side has a glue strength (0, 1, 2)-- finite number of tile types-- tiles join together if their glues match-- binding is stable if total strength ≥ a threshold

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Seed tile Boundary tiles

Rule tiles

Tile set for a sierpinski pattern self-assembly

OR

L-shaped seed structure

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(DNA) tile self-assembly

L-shaped seed

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Self-replication

Nature’s way of self-replication

Artificial self-replication

Sievers, D.; von Kiedrowski, G. Nature 1994

Cross-catalytic Auto-catalytic

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Tile Self-assembly and Self-replication

Tile crystal growth followed by fragmentation

Materials

Schulman R. et al. (2005), “Self-Replication and Evolution of DNA Crystals”

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Tile Self-assembly and Self-replication

Precise Gain

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Infinite Gain

Abel et al. “Shape Replication through Self-Assembly and RNase Enzymes”

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Tile Self-assembly and Self-replication

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Keenan et al. (2013) “Exponential Replication of Patterns in the Signal Tile Assembly Model”

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Problem Statement

Given a 2-D pattern of DNA tiles, how can it be self-replicated with minimal requirements

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Minimal Self-replicator Design

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L-shaped seed or target rectangular pattern (S) is gievn

M- Mold MTS- Mold Tile SetNSTS- Nano-Structure Tile SetS+M – Seed-Mold Complex

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Pre-assembled Corner Seed Tile (CST)Stable at T=2

Stable at T=2

SWitching Enabled Tile (SWET)

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SWETTile

Oregonator Oscillatort

Conc.

Inhibitor Signal

Oregonator Chemical Oscillator

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X2 X1

X2 + X1 Ø

X1 2X1 + X3

2X1 Ø

X3 X2

X3 Ø

Belousove Zhabotinski (BZ) reaction

k1

k2

k3

k4

k5

k6

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Oregonator Chemical Oscillator

Chemical kinetics to DNA-based CRN transformation (David Soloveichik, PNAS, 2010)

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ON-OFF Switching with inhibitor signal (X2)

Dynamics of species (X1 , X2, X3) Dynamics of X2

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Oregonator Chemical Oscillator

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Oregonator Chemical Oscillator

Parameter Scan: ON-OFF Switching of SWET

Applications of Self-replicator

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Apply Pattern Self-Assembly Tile set Synthesis (PATS) Patterns should be of same height A case of there patterns (P1, P2, P3) given below

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1. Self-replication of Multiple Patterns together

• Use self assembly to create molecular components• Make them in multiple copies using self-replicator

Applications of Self-replicator

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RAM

RAM Demux

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Applications of Self-replicator

Self-replicator-1 Self-replicator-2

Share same resource

Co-evolving molecular structuresSelf-replicator with higher gain would consume more resource

Conclusion

Minimal self-replicator can replicate rectangular patterns of tiles

Switching Enabled Tiles can be swtiched from ON to OFF by an Oregonator

oscillator

ON-OFF switching can be tweaked to meet the timing of splitting mold-seed

complex

Multiple patterns can be replicated together

Self-replicator may provide insights to the molecular selection principle that is

hallmark of everyform of life.

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Thank You

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