Estimates from Evolutionary Algorithms Theory Applied to Gene Design

The field of evolutionary algorithms (EAs) emerged in the area of computer science due to transfer of ideas from biology and developed independently for several decades, enriched with techniques from probability theory, complexity theory and optimization methods. Our aim is to consider how some recent results form EA theory may be transferred back into biology. It has been noted that the EAs optimizing Royal Road fitness functions may be considered as models of evolutionary search for the gene promoter sequences from scratch. Here we consider the design of synthetic promoters from the EAs methodology viewpoint. This problem asks for a tight cluster of supposedly unknown motifs from the initial random (or partially random) set of DNA sequences using SELEX approaches. We apply the upper bounds on the expected hitting time of a target area of genotypic space, the EA runtime, in order to upper-bound the expected time to finding a sufficiently fit series of motifs (e.g. binding sites for transcription factors) in a SELEX procedure. On the other hand, using the EA theory we propose an upper bound on expected proportion of the DNA sequences with sufficiently high fitness at a given iteration of a SELEX procedure. Both approaches are evaluated in computational experiment, using a Royal Road fitness function as a model of the SELEX procedure for regulatory FIS factor binding site. Our results suggest that some theoretically provable bounds for EA performance may be used, at least in principle, for a-priory estimation of efficiency of SELEX-based approaches.