Probabilistic RNA Designability via Interpretable Ensemble Approximation and Dynamic Decomposition

TL;DR

This paper introduces a new probabilistic framework and efficient algorithms for assessing RNA structure designability, providing tighter bounds and interpretability compared to previous methods.

Contribution

It develops a theory of ensemble approximation, a probability decomposition framework, and a linear-time dynamic programming algorithm for RNA designability analysis.

Findings

Tighter probabilistic bounds on RNA structure folding probabilities.

Efficient search over decompositions with linear-time complexity.

Enhanced tools for analyzing RNA structure design difficulty.

Abstract

Motivation: RNA design aims to find RNA sequences that fold into a given target secondary structure, a problem also known as RNA inverse folding. However, not all target structures are designable. Recent advances in RNA designability have focused primarily on minimum free energy (MFE)-based criteria, while ensemble-based notions of designability remain largely underexplored. To address this gap, we introduce a theory of ensemble approximation and a probability decomposition framework for bounding the folding probabilities of RNA structures in an explainable way. We further develop a linear-time dynamic programming algorithm that efficiently searches over exponentially many decompositions and identifies the optimal one that yields the tightest probabilistic bound for a given structure. Results: Applying our methods to both native and artificial RNA structures in the ArchiveII and Eterna100 benchmarks, we obtained probability bounds that are much tighter than prior approaches. In addition, our methods further provide anatomical tools for analyzing RNA structures and understanding the sources of design difficulty at the motif level. Availability: Source code and data are available at https://github.com/shanry/RNA-Undesign. Supplementary information: Supplementary text and data are available in a separate PDF.