Self-replication and Mutation of Polymeric Molecules Simulated by Simplified Chemistry

In this paper, we consider a simplified chemical model of self-replication and mutation processes of DNA-like polymeric molecules. Various cellular automaton models have been attempted to represent the self-replication process so far, in which only changes of chemical properties of the molecules are represented as discrete state changes. In the proposed model, the size and shape of molecules are taken into account, by introducing physical interactions among the elements represented as spring-mass-damper. Elements have discrete states like cellular automata, move in a continuous space, and undergo state transitions when an element approaches a certain neighborhood. Here, we designed a rule set for state transitions which realizes self-replication of any sequence encoded in a polymeric string such as single-stranded DNA. Brownian dynamics simulations were conducted to study how the density of the elements and local interactions among elements affect the self-replication process, especially mutation rate.