Extensions of Royal Road Functions for Use in SELEX in silico

The field of Genetic Algorithms (GA) in modern computer sciences has increasingly become a source of algorithms and methods for the computational systems biology. In this report we extend the definition of the Royal Road functions (specifically, their Royal Staircase version), used in GA, to BioRS functions, purposively devised to be applied in the computational biology. This approach is motivated by the necessity of taking into account the modular structure of biological macromolecules that has clear analogies with the theory of building blocks (BB) in GA. We demonstrate computationally how the BioRS functions can be applied to test the efficiency of different GA approaches with the BB preservation, using a multi-modular RNA-device as a test object. Particularly, we have shown that a simple version of the Hill Climbing algorithm (with random mutagenesis), RMHC, is extremely efficient. The impressively high efficiency of the RMHC algorithm in numerical experiments makes the question of its implementation in synthetic biology quite relevant. Our results can serve as a promising basis for the search for new effective techniques of the directed evolution in biology.