Design of a Minimal System for Self-replication of Rectangular Patterns of DNA Tiles Vinay K Gautam 1, Eugen Czeizler 2, Pauline C Haddow 1 and Martin Kuiper 3 1 Department of Computer and Information Science NTNU, Trondheim, Norway 3 Department of Biology NTNU, Trondheim, Norway 2 Department of Information and Computer Science Aalto University, Finland TPNC, 2014

2 DNA Self-assembly TPNC, 2014  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) 01

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: output: 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 TPNC,

(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 nm 2 ) Four sticky-ends (s 1, s 2, s 3, s 4 ) TPNC,

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 TPNC, 2014 Seed tile Boundary tiles Rule tiles Tile set for a sierpinski pattern self-assembly OR L-shaped seed structure 04

(DNA) tile self-assembly L-shaped seed 01 TPNC,

7 TPNC, 2014 Self-replication Nature’s way of self-replication Artificial self-replication Sievers, D.; von Kiedrowski, G. Nature 1994 Cross-catalytic Auto-catalytic 06

8 TPNC, 2014 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” 07

Tile Self-assembly and Self-replication Precise Gain TPNC, 2014 Infinite Gain Abel et al. “Shape Replication through Self-Assembly and RNase Enzymes” 08

Tile Self-assembly and Self-replication TPNC, 2014 Keenan et al. (2013) “Exponential Replication of Patterns in the Signal Tile Assembly Model” 09

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

Minimal Self-replicator Design TPNC, 2014 L-shaped seed or target rectangular pattern (S) is gievn M- Mold MTS- Mold Tile Set NSTS- Nano-Structure Tile Set S+M – Seed-Mold Complex 11 Pre-assembled Corner Seed Tile (CST) Stable at T=2

SW itching E nabled T ile (SWET) TPNC, SWET Tile Oregonator Oscillator t Conc. Inhibitor Signal

Oregonator Chemical Oscillator TPNC, 2014 X2X2 X1X1 X 2 + X 1 Ø X1X1 2X 1 + X 3 2X12X1 Ø X3X3 X2X2 X3X3 Ø Belousove Zhabotinski (BZ) reaction k1k1 k2k2 k3k3 k4k4 k5k5 k6k6 13

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

TPNC, 2014 ON-OFF Switching with inhibitor signal (X 2 ) Dynamics of species (X 1, X 2, X 3 )Dynamics of X 2 15 Oregonator Chemical Oscillator

TPNC, Oregonator Chemical Oscillator Parameter Scan: ON-OFF Switching of SWET

Applications of Self-replicator TPNC, 2014 Apply Pattern Self-Assembly Tile set Synthesis (PATS) Patterns should be of same height A case of there patterns (P1, P2, P3) given below 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 TPNC, RAM RAM Demux

TPNC, Applications of Self-replicator Self-replicator-1 Self-replicator-2 Share same resource Co-evolving molecular structures Self-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. TPNC,

Thank You TPNC, 2014