Random Structures and Evolution of Biopolymers A computational case study on RNA secondary structures

We compute large ensembles of RNA secondary structures by means of various computer algorithms. Their secondary structures are sorted and ranked. The number of neutral neighbours (i.e. one error mutants of a sequence that have the same structure with that sequence) are computed as well as the length of neutral paths (i.e. adjacent neutral neighbours). We calculate and compare correlation lengths which are a reasonable measure for the ruggedness of the sequence to structure mapping and describe the hardness of an optimisation problem. We investigate the innuence of size of the spaces as well as frequency and accessibility of structures on the degree of neutrality. We nd large neutral nets, percolating through sequence space even for rare structures and small alphabets. We conclude that the characteristic features of the mapping, namely the distribution of structures and the amount of neutrality are robust with respect to the chosen algorithm. This implies a new perspective on the eeciency of evolution by point mutations: from any random structure it is not far to any target and yet most mutations will preserve the structure.