Error propagation in the hypercycle

We study analytically the steady-state regime of a network of n error-prone self-replicating templates forming an asymmetric hypercycle and its error tail. We show that the existence of a master template with a higher noncata lyzed self-replicative productivity a than the error tail ensures the stabi lity of chains in which m<n - 1 templates coexist with the master species. The stability of these chains against the error tail is guaranteed for cata lytic coupling strengths K on the order of a. We find that the hypercycle b ecomes more stable than the chains only if K is on the order of a(2). Furth ermore, we show that the minimal replication accuracy per template needed t o maintain the hypercycle, the so-called error threshold, vanishes as root n/K for large K and n less than or equal to 4.