O3-6

Simulating Self-replication of Linear Structures
Taisei Mori 1

Ibuki Kawamata 1,2

taisei.mori.t6@dc.tohoku.ac.jp

ibuki.kawamata@tohoku.ac.jp

Satoshi Murata 1
satoshi.murata.a4@tohoku.ac.jp

12

Department of Robotics, School of Engineering, Tohoku University, 6 -6-01, AramakiAzaAoba,Aoba, Sendai, Miyagi, 980-0845, Japan
Natural Science Division, Faculty of Core Research, Ochanomizu University, 2 -1-1 Ohtsuka,
Bunkyo-ku, Tokyo 112-8610, Japan

Keywords: Self-replication, Virtual Spring Model, Transition rule, Autocatalysis
Self-replication is the process by which a system creates ones identical to itself without external
operations from outside. A typical example of self-replication is that of living organisms, but its
process is extremely complicated involving so many chemical reactions that it is difficult to see
what is essential in the process. Simulation models of self-replication help us to find out what are
the essential conditions for a system to replicate itself [1-3]. In order to describe theself-replication process, we have proposed the Virtual Spring Model [ 4], in which the bonds
between the elements are regarded as spring-mass-damper systems. In this model, the statetransition of each element is used to represent the chemical reactions among them.
By using this model, we were able to represent the self -replication system consisting of up to
three interconnected elements. As for the self-replication procedure, the use of catalytic elements
increased the success rate of self-replication, but the problem was that the number of transition
rules was too large despite the simplicity of the system. In order to achieve scalable
self-replication independent of the size of the system, the rules need to be redesigned.
Here, we propose a new self-replication procedure inspired by the concept of "complementarityof DNA", that only complementary base pairs (A and T, C and G) selectively bind to each other toform a double helix [5]. In DNA replication, an enzyme (polymerase) takes advantage of thisproperty to make a complementary copy of the strand. By representing the DNA replication
process with the use of autocatalytic procedure in the Virtual Spring Model, a scalable
self-replication system for linear structures can be realized. Under this framework, we present a setof transition rules and simulation results of self -replication of a strand (linear structure) formed byinterconnected elements with various sequences. We expect that the framework will be also usefulto establish self-replication systems of more complex structures and dynamic mechanisms.
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[2] K. Tomita, H. Kurokawa, S. Murata, “Graph automata: natural expression ofself-reproduction.” Physica D 171, pp.197-210, 2002.
[3] Z. Zeravcic, M. P. Brenner, “Self-replicating colloidal clusters.” PNAS 111(5), pp.1748-1753,2014.
[4] K. Fujibayashi, S. Murata, K. Sugawara, M. Yamamura, “Self-Organizing Formation
Algorithm for Active Elements.” IEEE, pp.416-421, 2002.
[5] J. D. WATSON, F. H. C. CRICK, “Molecular Structure of Nucleic Acids: A Structure for
Deoxyribose Nucleic Acid.” Nature 171, pp.737-738, 1953.