The information capacity of hypercycles

Details The information capacity of hypercycles The information capacity of hypercycles

2008-06-12

arxiv.org/abs/0806.2069v1

Biology

Quantitative Biology

Populations and Evolution

4 pages, 1 figure, submitted to J. Theor. Biol

Scientific paper

Hypercycles are information integration systems which are thought to overcome the information crisis of prebiotic evolution by ensuring the coexistence of several short templates. For imperfect template replication, we derive a simple expression for the maximum number of distinct templates $n_m$ that can coexist in a hypercycle and show that it is a decreasing function of the length $L$ of the templates. In the case of high replication accuracy we find that the product $n_m L$ tends to a constant value, limiting thus the information content of the hypercycle. Template coexistence is achieved either as a stationary equilibrium (stable fixed point) or a stable periodic orbit in which the total concentration of functional templates is nonzero. For the hypercycle system studied here we find numerical evidence that the existence of an unstable fixed point is a necessary condition for the presence of periodic orbits.

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