Combinatorial RNA Design: Designability and Structure-Approximating Algorithm

TL;DR

This paper characterizes which RNA structures can be designed with limited alphabets, provides efficient algorithms for testing designability, and introduces a structure-approximating method with provable guarantees.

Contribution

It offers complete characterizations of designable structures, linear-time algorithms for testing and constructing designs, and a novel structure-approximating algorithm for complex structures.

Findings

Complete characterization of designable structures with restricted alphabets.

Linear-time algorithms for membership testing and design construction.

A structure-approximating algorithm with a factor of two base pairs extension.

Abstract

In this work, we consider the Combinatorial RNA Design problem, a minimal instance of the RNA design problem which aims at finding a sequence that admits a given target as its unique base pair maximizing structure. We provide complete characterizations for the structures that can be designed using restricted alphabets. Under a classic four-letter alphabet, we provide a complete characterization of designable structures without unpaired bases. When unpaired bases are allowed, we provide partial characterizations for classes of designable/undesignable structures, and show that the class of designable structures is closed under the stutter operation. Membership of a given structure to any of the classes can be tested in linear time and, for positive instances, a solution can be found in linear time. Finally, we consider a structure-approximating version of the problem that allows to extend bands (helices) and, assuming that the input structure avoids two motifs, we provide a linear-time algorithm that produces a designable structure with at most twice more base pairs than the input structure.