The information capacity of hypercycles

TL;DR

This paper analyzes the maximum number of templates that can coexist in hypercycles, revealing how replication accuracy and template length limit the system's information capacity and stability.

Contribution

It derives a simple expression for the maximum coexistence of templates in hypercycles and explores stability conditions related to replication accuracy.

Findings

Maximum number of templates decreases with template length.

Product of maximum templates and length tends to a constant at high accuracy.

Stable coexistence can be stationary or periodic, with unstable fixed points linked to periodic orbits.

Abstract

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.