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RNA design aims to find a sequence that folds into a designated target structure under a specific RNA folding model, also known as the inverse problem of RNA folding. While numerous RNA design methods have been invented to search for sequences capable of folding into a target structure under the default (Turner) RNA folding model, little attention has been given to the identification of undesignable structures. This work bridges the gap between RNA design and undesignability by introducing a series of theorems and algorithms aimed at identifying both undesignable structures and their causative local structural components, which we define asminimal undesignable motifs. We first present theorems that provide sufficient conditions for recognizing undesignability structures and propose efficient, theorem-guided algorithms to verify whether an RNA structure is undesignable. While such global undesignability sheds light on the limits of RNA design, identifying the specific motifs responsible for undesignability is critical for understanding RNA folding models and advancing design methodologies. To this end, we develop a new theoretical framework for motif undesignability and propose scalable and interpretable algorithms to identify minimal undesignable motifs within a given RNA secondary structure. Our approach establishes motif undesignability by searching for rival motifs, rather than exhaustively enumerating all (partial) sequences that could potentially fold into the motif. Furthermore, we exploit rotational invariance in RNA structures to detect, group, and reuse equivalent motifs and to construct a database of unique minimal undesignable motifs. To achieve that, we propose a loop-pair graph representation for motifs and a recursive graph isomorphism algorithm for motif equivalence. Our algorithms successfully identified 24 unique minimal undesignable motifs among 18 undesignable puzzles from the Eterna100 benchmark. Surprisingly, we also find over 350 unique minimal undesignable motifs and 663 undesignable native structures in the ArchiveII dataset, drawn from a diverse set of RNA families. Last but not least, we demonstrate that our theory and algorithms can handle motifs with external loops—a critical advancement given the substantial impact of external loops on the quantity, diversity, and designability of RNA structure motifs.
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Undesignable RNA Structure Identification via Rival Structure Generation and Structure Decomposition
RNA design is the search for a sequence or set of sequences that will fold into predefined structures, also known as the inverse problem of RNA folding. While numerous RNA design methods have been invented to find sequences capable of folding into a target structure, little attention has been given to the identification of undesignable structures according to the minimum free energy ( ) criterion under the Turner model. In this paper, we address this gap by first introducing mathematical theorems outlining sufficient conditions for recognizing undesignable structures, then proposing efficient algorithms, guided by these theorems, to verify the undesignability of RNA structures. Through the application of these theorems and algorithms to the Eterna100 puzzles, we demonstrate the ability to efficiently establish that 15 of the puzzles indeed fall within the category of undesignable structures. In addition, we provide specific insights from the study of undesignability, in the hope that it will enable more understanding of RNA folding and RNA design. Availability: Our source code is available at https://github.com/shanry/RNA-Undesign.
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- PAR ID:
- 10673296
- Publisher / Repository:
- Springer
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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RNA design aims to find a sequence that folds with the highest probability into a designated target structure. However, certain structures are undesignable, meaning no sequence can fold into the target structure under the default (Turner) RNA folding model. Understanding the specific local structures (i.e., “motifs”) that contribute to undesignability is crucial for refining RNA folding models and determining the limits of RNA designability. Despite its importance, this problem has received very little attention, and previous efforts are neither scalable nor interpretable. We develop a new theoretical framework for motif (un-)designability, and design scalable and interpretable algorithms to identify minimal undesignable motifs within a given RNA secondary structure. Our approach establishes motif undesignability by searching for rival motifs, rather than exhaustively enumerating all (partial) sequences that could potentially fold into the motif. Furthermore, we exploit rotational invariance in RNA structures to detect, group and reuse equivalent motifs and to construct a database of unique minimal undesignable motifs. To achieve that, we propose a loop-pair graph representation for motifs and a recursive graph isomorphism algorithm for motif equivalence. Our algorithms successfully identify 24 unique minimal undesignable motifs among 18 undesignable puzzles from the Eterna100 benchmark. Surprisingly, we also find over 350 unique minimal undesignable motifs and 663 undesignable native structures in the ArchiveII dataset, drawn from a diverse set of RNA families.more » « less
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RNA design aims to find a sequence that folds with the highest probability into a designated target structure. However, certain structures are undesignable, meaning no sequence can fold into the target structure under the default (Turner) RNA folding model. Understanding the specific local structures (i.e., “motifs”) that contribute to undesignability is crucial for refining RNA folding models and determining the limits of RNA designability. Despite its importance, this problem has received very little attention, and previous efforts are neither scalable nor interpretable. We develop a new theoretical framework for motif (un-)designability, and design scalable and interpretable algorithms to identify minimal undesignable motifs within a given RNA secondary structure. Our approach establishes motif undesignability by searching for rival motifs, rather than exhaustively enumerating all (partial) sequences that could potentially fold into the motif. Furthermore, we exploit rotational invariance in RNA structures to detect, group and reuse equivalent motifs and to construct a database of unique minimal undesignable motifs. To achieve that, we propose a loop-pair graph representation for motifs and a recursive graph isomorphism algorithm for motif equivalence. Our algorithms successfully identify 24 unique minimal undesignable motifs among 18 undesignable puzzles from the Eterna100 benchmark. Surprisingly, we also find over 350 unique minimal undesignable motifs and 663 undesignable native structures in the ArchiveII dataset, drawn from a diverse set of RNA families.more » « less
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RNA design aims to find a sequence that folds with the highest probability into a designated target structure. However, certain structures are undesignable, meaning no sequence can fold into the target structure under the default (Turner) RNA folding model. Understanding the specific local structures (i.e., “motifs”) that contribute to undesignability is crucial for refining RNA folding models and determining the limits of RNA designability. Despite its importance, this problem has received very little attention, and previous efforts are neither scalable nor interpretable. We develop a new theoretical framework for motif (un-)designability, and design scalable and interpretable algorithms to identify minimal undesignable motifs within a given RNA secondary structure. Our approach establishes motif undesignability by searching for rival motifs, rather than exhaustively enumerating all (partial) sequences that could potentially fold into the motif. Furthermore, we exploit rotational invariance in RNA structures to detect, group and reuse equivalent motifs and to construct a database of unique minimal undesignable motifs. To achieve that, we propose a loop-pair graph representation for motifs and a recursive graph isomorphism algorithm for motif equivalence. Our algorithms successfully identify 24 unique minimal undesignable motifs among 18 undesignable puzzles from the Eterna100 benchmark. Surprisingly, we also find over 350 unique minimal undesignable motifs and 663 undesignable native structures in the ArchiveII dataset, drawn from a diverse set of RNA families.more » « less
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Abstract MotivationRNA design is the search for a sequence or set of sequences that will fold to desired structure, also known as the inverse problem of RNA folding. However, the sequences designed by existing algorithms often suffer from low ensemble stability, which worsens for long sequence design. Additionally, for many methods only a small number of sequences satisfying the MFE criterion can be found by each run of design. These drawbacks limit their use cases. ResultsWe propose an innovative optimization paradigm, SAMFEO, which optimizes ensemble objectives (equilibrium probability or ensemble defect) by iterative search and yields a very large number of successfully designed RNA sequences as byproducts. We develop a search method which leverages structure level and ensemble level information at different stages of the optimization: initialization, sampling, mutation, and updating. Our work, while being less complicated than others, is the first algorithm that is able to design thousands of RNA sequences for the puzzles from the Eterna100 benchmark. In addition, our algorithm solves the most Eterna100 puzzles among all the general optimization based methods in our study. The only baseline solving more puzzles than our work is dependent on handcrafted heuristics designed for a specific folding model. Surprisingly, our approach shows superiority on designing long sequences for structures adapted from the database of 16S Ribosomal RNAs. Availability and implementationOur source code and data used in this article is available at https://github.com/shanry/SAMFEO.more » « less
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