Evolutionary Optimization of Biopolymers and Sequence Structure Maps

Searching for biopolymers having a predefined function is a core problem of biotechnology, biochemistry and pharmacy. On the level of RNA sequences and their corresponding secondary structures we show that this problem can be analyzed mathematically. The strategy will be to study the properties of the RNA sequence to secondary structure mapping that is essential for the understanding of the search process. We show that to each secondary structure s there exists a neutral network consisting of all sequences folding into s. This network can be modeled as a random graph and has the following generic properties: it is dense and has a giant component within the graph of compatible sequences. The neutral network percolates sequence space and any two neutral nets come close in terms of Hamming distance. We investigate the distribution of the orders of neutral nets and show [10] that above a certain threshold the topology of neutral nets allows to find practically all frequent secondary struc..