Fluctuations Inherent in Hypercycles

Abstract

A general theory of fluctuations of the hypercycles is presented. Since the elementary process is inherently non-deterministic, the hypercycle is also subject to fluctuations. On the basis of the simplified model of Schuster and Sigmond, a set of coupled nonlinear Langevin equations is obtained. The analytical solution is given for the simplest case of the length n=2. The stationary distribution function is completely different from what is expected from the deterministric analysis, and it shows that the shortest hypercycle is “dead” at all.