SPATIAL GRADIENTS ENHANCE PERSISTENCE OF HYPERCYCLES

In this paper we study a partial differential equation model of cyclic catalysis of replicating entities (i.e. a hypercycle). In the presenc e of a spatial gradient in the decay rate of molecules we observe spir al drift towards the region of faster rotating spirals. On a radial gr adient one spiral anchors in the region of fastest rotation. If the dr op in the gradient is large enough, this spiral will break up in the p eriphery and form new spiral centres. The system settles in a dynamic equilibrium. This equilibrium turns out to be persistent even against strong parasites, i.e., molecules that receive increased catalysis but do not give any catalysis. If just one peripheral spiral manages to e scape the first attacking wave of the parasite, this spiral will gradu ally push out the parasites and in the long run the dynamic equilibriu m will be completely restored. We conclude that a gradient can supply regenerative power to the hypercycle.