Evolutionary Dynamics and Optimization

We view the folding of RNA-sequences as a map that assigns a pattern of base pairings to each sequence, known as secondary structure. These preimages can be constructed as random graphs (i.e., the “neutral networks associated to the structures”). By interpreting the secondary structure as biological information we can formulate the so-called “Error Threshold of Shapes” as an extension of Eigen’s et al. concept of an error threshold in the single peak landscape [5]. Analogue to the approach of Derrida and Peliti [3] for a flat landscape we investigate the spatial distribution of the population on the neural network. On the one hand, this model of a “single shape landscape” allows the derivation of analytical results; on the other hand, the concept gives rise to study various scenarios by means of simulations, e.g., the interaction of two different networks [29]. It turns out that the “intersection” of two sets of compatible sequences (with respect to the pair of secondary structures) plays a key role in the search for “fitter” secondary structures.